Yes. They can sometimes. The chances are low however. You may be better off going through in vitro fertilization.
Yes. Tubal reversal is successful in many cases. Certain types of ligation procedures however may not be reversible. Some tubes may also be too short after reversal reducing the chances of success. Your doctor should be able to discuss all these limitations with you.
Yes. Tubal reversals can be done successfully. The success rates depends on what type of tubal ligation you had in the first place. Your surgeon will want to review the notes from your original surgery if possible to plan the reversal. Some couples choose to do in vitro fertilization instead of a tubal reversal to get pregnant which is more expensive but has a higher success rate.