Two independent clauses that can each stand alone must be separated by either a period or a semicolon, or connected by a comma followed by a conjunction. Because this sentence doesn't include a conjunction like "and" after its comma, it is incorrect. (This error, where two independent clauses are incorrectly connected by a comma, is known as a "comma splice.")

The clause, "however, he wouldn't meet her eye," is an independent clause and must be separated by a semicolon or a coordinating conjunction.

This is a run-on sentence. The two independent clauses need to be split into two separate sentences, or separated by a semicolon.

A comma should only be used to separate an independent clause from a dependent clause: here it is separating two independent clauses, so a period or semi-colon is more appropritate.

This is an example of a comma splice. The two independent clauses should be separated by a period, a semi-colon, or a comma and a conjunction, not by just a comma, which is used to separate independent and dependent clauses.

The first clause of this sentence, "How many times do I have to tell you," is actually a rhetorical question.  It is an independent clause and therefore must be separated with stronger punctuation than just a comma.  In this case, it would be appropriate to set it off as its own sentence, ending in a question mark, but regardless, the comma splice in "you, you" is what makes this sentence ungrammatical.

A comma cannot be used by itself to join two independent clauses, so "substance, it" contains this sentence's error. The first independent clause in this sentence is "Baking soda, also known as sodium bicarbonate, is a truly useful substance." The second independent clause is "It can be used for cooking, baking, and cleaning." Two independent clauses can be joined into a compound sentence in one of two ways: by using a comma followed by a conjunction or by using a semicolon.

This sentence is an example of a run-on or comma splice. It has two independent clauses separated only by a comma. One way to fix this is to change the comma to a semicolon; if this were to be done, the corrected sentence would read, "Thomas had always struggled with trigonometry; he thought that circles should remain circles and let triangles and squiggles be their own shapes."

The clause, "she refused to speak with him for longer than necessary" is an independent clause and therefore must be separated from the sentence's initial independent clause ("Cal, with his good looks and smug tone, came off as arrogant to Sarah") with a semicolon, a comma followed by a conjunction, or a period, not just a comma.

The clause following "them" ("they were such huge fans of those shows") is an independent clause. It therefore needs to be joined to the first part of the sentence, the compound independent clause "I don't remember many Saturday morning cartoons, but May and John can name pretty much all of them") using a semicolon, a comma followed by a conjunction, or a period, not just a comma. (Note the correct use of a comma followed by the conjunction "but" in the sentence's initial compound independent clause.)