Anyone and everyone can. It is a matter of public record and even the BK has the obligation to make sure all interested parties have the info.
It should be on a W-2 if you have received one from them.
Yes. Employers can find out almost anything about you.
If possible, follow them to work, or have someone else follow them to work.
The best source for a complete list of previous employers is to go to your local social security office. They can give you a complete list and time that you worked there. I believe this is free I had...