Does Would you mind and do something instead of Would you mind doing something sound acceptable in spoken AmEng, or is it an attempt to imitate or render colloquial speech in not so formal writing?
1.) "Would you mind and do something?"
2.) "Would you mind and provide the phone number connected on the account?"
3.) "Would you mind and tell us what you've tried."
According to my ear, there's nothing wrong with those types of expressions. (I'm an AmE speaker, and I've traveled to or lived in most corners of the USA.)
Actually, in my personal opinion, I'd consider those versions to be more polite than these alternatives:
"Would you mind doing something?"
"Would you mind providing the phone number connected on the account?"
"Would you mind telling us what you've tried."
as those last three versions have the speaker sorta already assuming that the other person won't mind hearing a request from him, and the speaker is rushing a request at the other person. (Though others might disagree.)
As for the OP's #1, #2 and #3 examples, I've heard these kinds of phrases spoken often by AmE speakers, and I'm pretty sure I've used them myself. E.g. "Would you mind and do something for me?"
I'd consider these kinds of expressions to be at least of an informal style of standard English. The coordinator "and" has many uses, e.g. "Be sure and lock up", "We always try and do our best". (There might be some related info in the 2002 reference grammar CGEL.)
"Would you mind and do something" is unacceptable in any region of the US in which I have ever lived (Northeast, Mid-Atlantic, South, Mid-west and Northwest.) It is not idiomatic, and at best is a terrible example of attempt at simulating non-native speech.
Googling "would you mind and do" turns up no examples of this phrasing except your own question. The most common hit is for two polite phrases
"Would you mind" and "do you mind"...
We do have bizarre idiomatic speech pockets (as with PA Dutch), but none quite that bizarre.
I was interested in seeing what use authors have historically made of the construction "mind and [other verb]," along the lines of the poster's wording "would you mind and do something." So I ran Google Books searches for three phrases—"now mind and," "mind and do," and "you mind and"—for the period 1600–2008. These searches yielded quite a few matches, going back to at least 1721 and continuing (probably) until at least 1947.
However, none of the matches attempt to connect mind in the sense of "disapprove" or "object" or "be unwilling" (which appears to be the sense of mind that the OP intends) with another verb via a conjunctive and. Instead most of the relevant instances use mind in the sense of "pay attention" or "remember" or "obey."
Examples from England, 1721–1908
Examples of this usage go back to England in the early 1700s. From James Naylor, A Collection of Sundry Books, Epistles and Papers Written by James Nayler (London, 1721):
High carnal minds seek high things, and so they grow lofty and proud, and such God resists, and keeps them afar off: but the poor in spirit seek truth and meekness, and are fed thereof at the table of the Lord; meek, and lowly and just, and faithful are all his household, who feed and sup with him. Now mind and consider your ways, who are gone out unto the mountains to worship and feed yourselves, you may read of Israel's sin in going out from the temple, in which the Lord had said he would dwell, and be enquired of, and they built altars without him, and there called upon him but found him not, for which he rejected their worships, and their temple also.
From Edmund Calamy, A Continuation of the Account of the Ministers, Lecturers, Masters and Fellows of Colleges, and Schoolmasters, who were Ejected and Silenced after the Restoration in 1660 (1727), citing a letter of unidentified date:
Keep close to GOD daily. Mind and do his Work thoroughly, and you will find 'tis most delightful. Find out and close with some pious, studious, ingenious Youths, and make them your familiar Acquaintance. Take heed you neglect not publick holy Duties. Remember the Sabbath to sanctify it.
From Isaac Penington, The Works of the Long-Mournful and Sorely-Distressed Isaac Penington, volume 2, second edition (London, 1761):
Now mind and remember this which followeth:
From a letter of August 12, 1808, in Extraordinary Life and Character of Mary Bateman, the Yorkshire Witch, twelfth edition (Leeds, 1811).
MY DEAR FRIEND.—I send you these few lines to let you know that I shall get to Wittwell in Boland on Friday next, so I could wish make yourself happy thou love of mine, till thou see me tap thy shoulder for it would not do for the to know the moment, for it would put the in such fear and do not let Mary reed this letter of freedoms, for I have not wrote to hr for a long time, and for her husband i not likely to get no better and he says it is long of you and wont hardly let her stur, you may tell her to make her self easy on me not sending to her, it is for a reason, now mind and bury this near the other.
From The Novitiate's Preceptor; Or, Religious and Literary Register for the New Church, volume 1 (London, 1827):
May I put him [a dead squirrel buried in a china vase] into a halfpint stone-mug that is in the house, and then fasten the top of this box over it? Aye, aye, replied Mr. Rotchford, you may do that if you please; so away ran Kitty for the stone mug, and Charles for the spade, with which he directly began to dig for the squirrel. Take care, Charles, said his father, mind and do that carefully, or you will break the tureen and all your labour will be useless.
From a letter from James Rush to his son James (April 20, 1848), in An Introductory Narrative and a Revised Report of the Trial and Execution of J. B. Rush (1849):
Direct for me at the Shoreditch station, and mind and write me a long letter of every thing that has taken place. If they have token possession, mind and do not let them take anything away, or meddle with any of my papers; but as I said before, if they are not yet on, keep them out of the house at all events till you see me on Sunday morning, and do not let any one know when I am coming.
From Andrew Lang, "Brother and Sister," in The Red Fairy Book (1893):
'Sister, open the door, I must get out.'
So sister opened the door and said, 'Now mind and get back by nightfall, and say your little rhyme.'
And from Kenneth Grahame, The Wind in the Willows (1908):
When we are through [the tunnel], I will shut off steam and put on brakes as hard as I can, and the moment it's safe to do so you must jump and hide in the wood, before they get through the tunnel and see you. Then I will go full speed ahead again, and they can chase me if they like, for as long as they like, and as far as they like. Now mind and be ready to jump when I tell you!
Examples from North America, 1725–1887
Similar examples appear in letters by colonial Americans by 1725 and in books by American authors by 1825. From a modern history citing a letter by JC [James Crokatt?], August 24, 1725, in The Southern Frontier, 1670–1732 (2004):
It was an Indian, the head warrior of Tennessee, who, according to Colonel Chicken, agent at the same period among the Cherokee, 'got up and made the following Speech to me and the People of the Town. "That they must now mind and Consider that all their Old men were gone, and that they have been brought up after another Manner than their forefathers and that they must Consider that they could not live without the English."
From A Lady, Stranger of the Valley: Or, Louisa and Adelaide (New York, 1825):
Laluce strongly opposed this measure [a plan of action suggested by uncle Charles], for he greatly feared they would refuse to bestow their incomparable daughter on a person who had so long depended on their bounty, and whose connections they were unacquainted with; but uncle Charles insisted on having his way, or he would do nothing about it, and Laluce was obliged to submit.
"Now mind and work your card right," said the delighted uncle Charles, "and if you fairly set out for it, my dear boy, you can make up a story equal to any one."
From Susanna Moodie, Richard Redpath, in The Literary Garland, and British North American Magazine (Montreal, October 1843):
"Well, well, Bess! You may have him," returned the planter. "But you spoil all your slaves. Now mind and keep a strict eye over him. If he is such a good cook, he will spare you a world of trouble."
From Theodore Fay, Hoboken: A Romance of New York, volume 1 (1843):
"Pooh, pooh, Katy! what a superfine Spartan mother you would have made! I fancy your presenting Frank his shield and telling him 'with it or upon it!'"
Mother would say," interrupted Mary, laughing, "'with it or without it! but, at all events, do you mind and come home!'"
From Joanna Mathews, Belle Powers' Locket in Little Sunbeams (London, 1872 [but Mathews was born in New York, and wrote and lived in the United States]):
A door in the side of the garden wall opened upon the street which bounded one side of it; and, unfastening this, the cook passed out,saying to Marcia,—
"Now mind and keep the door shut; and don't you be poking your head out, and leaving your work."
From Mrs. S.E. Dawes, "Out in the Cold: A Story for Girls," Our Boys and Girls (New York, April 1873):
"We are well met," said he, "for I have something to say to you, Kate Somers. Now that some one has at last given you a home, do you mind and keep it. If you don't like, you needn't think of going back to the city, for no one will take you at the Home you left."
From "Buds, Blossoms & Leaves," in Popular Gardening and Fruit Growing (Buffalo, Ne York, October 1886):
Now mind and plant your bulbs, mainly in clumps, each sort by itself.
From Grammar School, issue 6 (Chicago & Boston, 1887) [combined snippets]:
I had it [a night-cap] off in a second, and I saw my mother's basting threads in the hem. She seemed very near me, somehow, as I sewed and sewed, until it was really finished at last. But every stitch I put in had the same word to say for itself. One said, "Now mind, and finish the next thing!" And another one said, "Now mind and finish the next thing!" And another one said, "Now mind and finish the next thing!" until I got pretty tired of it.
The reason "Would you mind and do something" sounds vaguely plausible as colloquial American (or British) English is that the wording "mind and [do something]" was in at least occasional usage in parts of the English-speaking world for at least a couple of centuries. But two points are essential in accurately appraising the significance of this fact.
First, the recorded usage of the phrase involves mind being used in the sense of "pay mind to"—that is, "pay attention" or "remember" or "obey." That is not at all the meaning of mind in the OP's example; there, the meaning is "disapprove" or "object" or "be unwilling." But in the dozens of relevant matches that Google Books found in the searches I conducted, the construction "mind [as a verb] and [some other verb]" never used mind in that sense.
Second, the Google Books results strongly suggest that the "mind and [another verb]" formulation has rarely been used in published writing in the past century, and that the wording is moribund. The last example from the United States that seems to use the phrase in the old way is Marguerite McIntire, Carey Brown (New York, 1942):
"I'll give you a small pail to pick into," Mrs. Steven said, "and a larger one for dumping in. You've got to pick clean. I won't pay you anything for dirty berries; no sticks, no leaves, no green ones. Now mind. And pick with the tips of your fingers so's you won't rub the bloom off. Think you can do it all right?"
And the last British example may be from The National Review: The English Review (1947):
"Here you are, Sir, they were no' quite dry before. Now mind, and fold the meat this way, John, or you'll lose the blood. This label's no' on firm enough — I'll re-tie it." She looked fine, Mrs. Goodwins, in her spotless white overalls, with her laughing eyes.
So strike one is that historically "mind and [another verb]" never used mind in the way that the OP wants to use it. Strike two is that usage of the wording in the way that was fairly popular once upon a time has dropped off considerably since the late 1800s. And strike three is that the OP not only wants mind to mean "disapprove" or "object", but also wants to frame the wording as a conditional question. Here again, the Google Books search results do not yield a single match that illustrates similar manipulation of the phrasing to pose a conditional question.
Taking all of these considerations into account, I think that the OP's wording may stir readers' memories of superficially similar wording in The Wind in the Willows, The Red Fairy Book, and elsewhere—and thus may strike those readers as being potentially valid as colloquial language from somewhere else. But there is no record of a genuinely similar usage in Google Books, and I think the OP's wording has probably never been used un-self-consciously by a colloquial English speaker in North America or the UK.
AmEng here. Would you mind and do something sounds entirely bizarre to me.
To me, the definition of "mind" in these cases is "to be annoyed or upset about something." -- Substituting that definition, the "and" separates the verb that would be annoying. It makes no sense:
Would you be annoyed and provide the phone number?
Would you be annoyed providing the phone number?
On the other hand, perhaps this has some relation to the colloquial expression "try and do" vs. "try doing" : see a related answer.
The expression is “would you mind to … ?”
“Would you mind?” means “would it bother you?”
Would you mind [to] provide the phone number connected [with] the account?
Would you mind [to] tell us what you've tried?
Would you mind [not to] steal my Sig?
Would you mind [not to] repeat that to anyone?
So it is “Would it bother you not to repeat that to anyone?”
In American English, it is more common to hear it like this, though:
[Do] you mind [providing] the phone number connected [with] the account?
[Do] you mind [telling] us what you've tried?
[Do] you mind [not stealing] my Sig?
[Do] you mind [not repeating] that to anyone?