GMAT rules for 'which' and 'that' usage

april24 wrote:
1- Should 'which' and 'that' ALWAYS touch the noun they modify? If no, what are the exceptional cases?

There are acceptable constructions in which which or that is not exactly next to the noun being modified.

For instance, there can be words that modify the noun and come between the noun and which.

That dog of Fred's, which came from a shelter, is so happy to run in the park.

In this case, which came from a shelter clearly modifies dog.

2- Should 'which' ALWAYS follow a comma (except when it follows a preposition)
and 'that' should NEVER follow a comma? If no, what are the exceptional cases?

While which almost always follows either a comma or a preposition here is an exception.

In order to choose the best answer, one has to determine which of them matches what the passage says.

That can follow a comma in certain situations.

For instance, in certain cases something can be inserted between the noun and that, and you need commas around what is inserted.

The goat, of all things, that ate the cake was the cause of all the trouble.

Without that inserted phrase, there would be no comma before that.

The goat that ate the cake was the cause of all the trouble.

Notice, this is all logical, and so even if you were to have seen these constructions on the test before seeing this explanation, you could have figured out that they were ok. Generally speaking, in SC, logic trumps simplistic application of supposed rules.