Yes. . Numbness is a sensory phenomenon. Pushing occurs through activation of muscles by motor nerves. Thus, if you are numb, you may still be able to push. Further, a lot of the pushing comes from bearing down, which you should be able to do well even with a strong epidural. The best advice is to have your epidural adjusted during labor so that when you are ready to push, it is as dense as you want.
Yes but differently. Usually the anesthesia team strives to achieve good pain relief but not so much numbness that you lose all sensation and the urge to push. The reason that an epidural catheter is usually inserted through the epidural needle and left in place for childbirth is to allow small short-acting doses of local anesthetic to be used. In this way the doses can be adjusted up or down as needed.