I am in the same boat. I've talked to my Ob/Gyn extensively about it. Depending on how much of the tubes are left, tubal ligation reversal is possible. The other option is IVF. She recommended IVF if we only want one pregnancy,and reversal if we wanted to be pregnant multiple times in the future. I'm actually opting for the reversal because I have 2 children but he has none.
I am not sure. That is something that you might want to ask you doctor....usually the answer would be no....not by conventional methods. However, there are alternatives like ivf. You should probably speak to your doctor who can refer you to a fertility specialist, if necessary.
Good luck! :)