I read it in a website and it said "Any and all persons can have this account".
It does not roll off the tongue and something seems amiss. Is this right usage of "any and all"?
There are contexts in which the phrase any and all may serve a purpose, but this is not one of them; in fact, in this case, the sentence, interpreted literally, means something that was unlikely to have been intended.
Consider first a slightly different case. Suppose that the website said 'Any and all students of this university can have this account.' What would that mean? The word any would in that case tell us that there are no special requirements for having the account, other than being a student of this university. Would the word all add anything to that? Yes, it would. It would tell us that the capacity of whatever the accounts are for is such that it can accommodate all the students of the university. If the capacity were limited (e.g. the server would crash if every student really opened the account), it would be true that any student can have the account, but false that all students can have it.
In this case, however, the sentence is not about some relatively limited set, as the students of a particular university, but 'persons', without any qualification. What the operators of the website probably wanted to say is that there are no special requirements for opening the account. That could have been adequately expressed by their saying 'Any person can have this account'. They have instead said 'any and all', perhaps because they vaguely remembered having seen that phrase in some legal document and because it sounded more impressive to them. If they thought about the matter more carefully, however, they would have realised that saying that all persons can have the account means that whatever the accounts are for has sufficient capacity to accommodate all human beings currently in existence. It is unlikely that they actually intended that.
It doesn't sound quite right, does it?
According to the Cambridge Dictionary:
Persons (plural) is a very formal word. We only use it in rather legalistic contexts:
[notice in a lift] 'Any person or persons found in possession of illegal substances will be prosecuted.'
The context doesn't seem very formal, so perhaps it should be rewritten as "Any and all people can have this account." But it's more idiomatic to say "Anyone and everyone can have this account". Or maybe just "Anyone can have this account".
[By the way, 'it rolls off the tongue' is the standard expression.]
"Any and all" creates a tautology. You should just pick one. "Any person can do this" or "All persons can do this".
Personally I would go with the first one.
The phrase "any and all" is common in legal documents. Recently, the Court has again held that "[alny means 'every,' 'each one of all,' and is unlimited in its scope." Parker v Nationwide Mutual Ins Co, 188 Mich App 354, 356; 470 NW2d 416 (1991) (quoting Harrington v InterState Men's Accident Ass'n, supra).
https://www.michbar.org/file/generalinfo/plainenglish/pdfs/91_oct.pdf