Induction of labour requires some indication. Like post dated pregnancy, Diabetes, Hypertension etc. If your pregnancy has no complications then no need of induction. And success of induction depends upon Bishop's score( per vaginal assessment &history points). Chances of failure of induction and then Cesarean are more if induction is done with poor Scoring.
Epidural: Surely you can take it once you are in established labour, like 3-4cms Dilatation if cervix. It do help but at last push, u need to stop it. Chances of Forceps or Vacuum delivery are more.
Do you have any complications in pregnancy like diabetes hypertension etc
If no complications you can wait till due date which is 40 wks and if no spontaneous onset of labour then induce at 40 wks
If you have complications then after 37 wks anytime you can induce and deliver
Sure epidural can be administered during induction