No. There is no word in English that always requires a comma before it.
Yes.
A comma is typically used before "but" when it connects two independent clauses. However, if "but" is joining phrases within a single sentence, a comma is not necessary.
When which is used to introduce a nonrestrictive adjectivial clause it must it must follow a comma. But there are numerous examples where which does not need to follow a comma. Including: Which melon do you want? I can't tell which melon to buy.
In general, you do not need a comma before a preposition unless it is part of a larger phrase that requires punctuation. However, always defer to the specific rules of grammar or style guide you are following.
Yes
,Always.
No, it is not always necessary to put a comma before the word "so that." The use of a comma before "so that" depends on the sentence structure and whether it is separating independent clauses or introductory phrases.
You do not always need to use a comma with the word sobut if you do, it is best to only use the comma before the word. An example is "The travellers faced a long drive home, so they decided to stop at MacDonald's first."
As always, I enjoyed my time with the kids.
No, a comma before "as appropriate" is not necessary. It depends on the context of the sentence and whether it flows better with or without the comma.
Yes
In the U.S., "e.g." almost always needs a comma before and after. (According to the Chicago Manual of Style and others.) Usually when we say, "for example," before listing examples, we offset "for example" by commas. An abbreviation meaning the same thing is no different. But I understand that in the U.K. they often leave out the comma. I can't verify that.