It may help to recognize two things -- 1) punctuation is not a matter of grammar; it's a matter of style and 2) the purpose of punctuation is to help readers parse a linear string of text into a parse tree. With respect to point number 1, there is no "right" or "wrong", just "helpful" or "unhelpful" in pursuit of point number 2. To the end of point number 2, various organizations academic, journalistic, and otherwise have developed manuals of style with lists of rules. All good manuals will acknowledge that it's impossible to state definitively in all situations whether a rule applies, that exceptions will necessarily arise, and that at times a writer's judgement and discretion may trump any rule.
One of the longer subsections of these manuals deals with the comma, which mark is tasked with making many and varied classifications. Sometimes conflicting demands make it difficult to know where or if to place a comma. I'm afraid that your Wikipedia quote is unhelpful as a "general" rule. You can tell because the statement is followed immediately by a description of the comma's role in lists. So if Ricky says,
I'm dumb, obtuse, ignorant, and French
commas separate the adjectives, with some people leaving out the last, but if he'd said
I'm dumb and obtuse
no one would advocate placing a comma after dumb. Does the strength of the "grammatical linkage" between the two adjectives change from one version to the next?
Let's examine your sentences
- The player to the right of the dealer turns up a card, and frowns.
One job of the comma is to warns the reader that one independent clause is ending and another is beginning. So generally, compound grammatical objects that don't rise to the level of clauses, like compound predicates are not separated by commas. But another job of the comma is to warn the reader away from a wrong parse. The linguist Steven Pinker calls these "garden paths" because they lead the reader to the wrong grammatical decision. Here, you don't want your reader to see the and and ready himself for
1a. The player to the right of the dealer turns up a card and the
But you also don't want the reader to expect
1b. The player to the right of the dealer turns up a card, and frowns
appear on the faces of the others.
You can't use one comma to give both warnings. So it's your call until your editor overrules you.
- He'd already clumsily thumbed a plastic slip onto a thick drop of glycerol, so as to crush the knot of a spider.
I'll have to say that this sentence made the least sense to me until your explanation, but it still didn't matter. Another rule of the comma is to separate a non-restrictive clause. Like all these rules, they exist to guide parsing, which is to say that they can't help with the semantics. Did you mean that the crushing is the defining characteristic of the drop of glycerol? If so, then no comma, the infinitive is restrictive. Did you mean, "Oh, by the way the spider got crushed"? If so, then the infinitive is nonrestrictive, merely informative, and no comma is appropriate.
On to your last example
- By the succulent he planted and replanted to pass the time, is a china bull.
Commas generally set off introductory adverbial phrases and introductory participial phrases that don't immediately precede the verb. But you've designed a sentence to defeat both rules. In fact, although "planted and replanted" may look participial to a reader who, having long forgotten the introductory preposition by, struggles to the is, the compound predicate actually belongs to a reduced relative clause modifying succulent:
3a. ... succulent [that] he planted and replanted to pass the time....
Commas cannot avail you or your reader here, and a rephrase is the best thing you can do for your prose and the kindest thing you can do for your reader:
There is a china bull placed by the succulent he planted and replanted to pass
By the way, the manual I use is the Chicago Manual of Style, so the rules I cite are the ones you'll find therein.