Yes. Just ask your gynecologist to coordinate with your plastic surgeon- shouldn't be a problem.
Yes, but... Assuming that this is an elective tubal ligation, it would be fine to get a tummy tuck at the same time. If you were to get a tubal ligation in the immediate postpartum period, i think most plastic surgeons would hold off on doing the tummy tuck. The skin would need to get back to an "unstretched" state before an accurate tummy tuck could be done.
Yes. Routinely done.
Yes. Great idea, but must be ok with OB gyn who is to do that part. If the plastic surgeon consults the OB gyn it's usually "yes".