I know a lady that was in the military and she was making a career out of it. She was married, but did not want to have any children. 7 - 9 years after she had a tubal done she got pregnant.
If the tubes were "banded" and not cut/burnt, the bands can loosen, opening the fallopian tube. This is pretty rare, and the likelihood of this happening depends on the material used.
Very slim. It is possible, but tubal ligation is to prevent your egg from reaching your uterus. If there is no egg, there's nothing for the sperm to fertalize. However, some woman have become...