comma + ing can be used to present the idea that something is the consequence of the past action.
Absolutely. That's a really common use of the comma -ing modifier.
"And" connect 2 independent actions or objects.
Where did you get this rule from? It's much too restrictive. One of the problems (and advantages) of language is that it's not as precise as, say, algebra. We can use the word 'and' in lots of different ways. We can use it for independent or related actions, simultaneous or sequential actions, and for other constructions too.
John jumped out of the building and died instantly.
John jumped out of the building, dying instantly.
I'd say that both of these sentences are correct. (Although, to be pedantic, presumably John died not instantly, but a few moments later.) What seems to be different is the
emphasis. The second sentence emphasizes the causal connection, the first just implies it. However, that's far too subtle to be tested on GMAT.
In conclusion, take care that you don't make up complicated rules that don't really exist. Also, be sure to check first for cruder issues than nuances of meaning when solving SC problems.