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i dont think anyone actually cares unless you are in english class or someone wants to feel smug on the internet (you can ignore the 2nd one completely).
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Informally, commas are "misused" regularly even by native writers, and almost no one notices or cares unless the misuse is frequent and egregious.

Formally, most comma use is an issue of style, not grammar, and style guides differ on when they should and shouldn't be used. The main rule that's actually a matter of grammar is this: commas cannot be used to join two "clauses" (phrases which could be independent sentences) without a conjunction.

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So putting the commas in "I'm eating a hot dog, she's listening to radio, we are having a wonderful time." is grammatically wrong? TIL, I guess.
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English has no central authority, so the lines between grammar and style can get fuzzy. Most guides would say you need an "and" after the second comma, but some make an exception if the clauses are "very short and alike in form". See Wikipedia's article Comma splice if you are interested in the pedantics. https://en.wikipedia.org/wiki/Comma_splice
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You still didn't answer: am I supposed to write "I'm eating a hot dog she's listening to radio" without a comma for that sentence to be grammatical? Or am I supposed to always insert "and" into it?
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With or without a comma, without a conjunction like "and" the example is a run on sentence and is ungrammatical. You should join the clauses with a conjunction, and including a comma before the conjunction is a common style.

There's a caveat where some style guides permit using a comma without a conjunction in specific contexts, but most don't.

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Don't worry about it.

The lack or excess of commas doesn't upset any reasonable person in the slightest.

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You're doing fine. English grammar pedants speak infrequently. Mostly due to the disinterest of the listener.
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As a native English speaker, same.
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