1. If, after petitioning to adjust your status, you get employment authorization (EAD), you will be able to get a social security number.
2. It will take as long as it takes. You can check current processing times here - but they're averages, not a promise that yours won't take longer. At present, if you leave before you get your Green Card you're looking at a three year period of ineligibility to return. Once you hit the one year mark for your overstay, that goes up to ten years. So you will want to stay in the U.S. while this process continues.
3. The process, discussed in more detail in dozens if not hundreds of threads in this forum, is to get married then petition to adjust your status on the basis of marriage.

