Ripan - you have already got the answers to the (multiple) questions you posed. It would appear that you either dont like the answers or you despair that there is a degree of uncertainty surrounding them. Get used to it. Nobody is going to guarantee you a CFI job after training or commit to sponsoring you for residency.
Why the hell would they when there is so many US CFI's who would give their eye teeth for a job. Presumably you have checked the US State Department website and have discovered that you must leave the country after expiration of your visa and any extensions granted. Presumably you also know from the same source that an employer would need to demonstrate that you possess a skillset which cannot be obtained by employing a US national. What is that skillset likely to be - you can fly an aircraft???????????
So stop fishing for angles here - you will not find any workarounds to a fairly rigid procedure. You have enough information to make your choice. The US FTO's have been honest with you by saying that any employment will be subject to a successful interview (and perhaps availability of a job and demonstration of a stellar training record would help).
So get on with it or enrol in an FTO closer to home. And to answer your question re 'what is GA' on another thread - google General Aviation - you really, really should know that.