When will I be allowed to start eating after birth?

Depends. If vaginal delivery once the delivery procedure is over, if c section start with fluids then increase diet as tolerated.
Depends on type. If you have a vaginal delivery, you may start eating as soon as the placenta has delivered. This is a precaution in case the placenta will not deliver and you need a procedure. If you have a cesarean section, you may be allowed to have ice chips, but you will probably not be able to eat for 8 or 12 hours. Some physicians like to wait until you pass gas to show that air is going through.