Yes. There are times to be a hero & avoid drugs. This is not one of those times. If a woman has no or few medications in labor, it is very reasonable to have a small amount of local anesthetic injected into the tissue where stitches will be placed. Pain is not always healthy, and after going through labor she should have anesthesia if agrees after being informed of risks/benefits by providers giving it.
No. If you do require stitches after delivery, you will be fine. If you've had an epidural during labor this can provide enough anesthesia to help during the repair. If not, your doctor/midwife can give you a shot of local anesthetic to provide pain relief. You should know however, that sometimes you'll feel tugging, pulling or pressure while not feeling pain. This is normal and common.
No. Typically, if you have chosen an epidural you will have little sensation if a tear or episiotomy is repaired. If you have been anesthesia-free or your epidural is not decreasing your sensation, your doctor will inject some local anesthetic to the area to be sewn. You may feel a pulling or tugging sensation as the stitches are pulled tight or tied but should not feel sharp pain.
No. If you tear, your doctor should use anesthetic before sewing you up. If it doesn't work, say so and he'll give you more. If you have an epidural, you won't need more anesthetic to be sewn up. Of course, if you're talking about being sewn up after a c-section, you'll be under spinal or epidural anesthesia. With an episiotomy, you'll get local anesthesia before the cut is made.