1) Whats wrong with this construction "The blizzard deposited more than a foot of snow on the train tracks, and prompted the transit authority to shut down service temporarily, causing discontent among commuters who were left stranded for"hours."
Yes, I agree that your version is an acceptable solution. We could have the parallel structure X and Y, and the follow it with a comma -ing modifier. However, I think that this solution is slightly less logical than the one given in the strategy guide. After all, the "prompting" and the "causing" are two results of the blizzard, although I think the difference in meaning is too subtle to be tested on a GMAT problem.
2) It is given that we can join two independent clauses with ",and" or ";" but can ",and" also be used to connect and independent clause with a dependent clause ?
Not sure if I understand you. Certainly, you can use 'and' to join two potential sentences together. But rather than thinking of joining an independent and a dependent clause, I would understand this as a 'parallel construction'. After all, in the (correct) sentence 'Amir went shopping and bought some bread.', I wouldn't describe 'bought some bread' as a dependent clause, but as a parallel element that links to 'Amir'.
3) If an independent clause has a subject and a verb is it compulsory for it convey a structured meaning for it to be termed as an independent clause ?
I don't know what 'structured meaning' is. Generally, if we use 'and' in a sentence, there will be some relationship between the parts. It would sound pretty random to say 'The Earth has one moon and ants are small.' However, that's "grammatically" okay. I guess we could contrive a situation in which that sentence had a place (perhaps as an answer to multiple quiz questions). The basic point is that meaning has context, and you'll see the kind of logical traps that GMAT sets by trying out a few problems.
Can we somehow
This is tantalizing.