Yes, besides, it is not uncommon for a bullet to fail to pierce the skull and did not cause instant death. Therefore, they usually shoot through the mouth at an angle of 45 degrees. And the execution is carried out by a shot at the base of the skull from the back.
There is such a possibility. The temple is a very vulnerable spot, but there have been cases when a bullet passed through the brain without killing it. But the pain must pass from the nerve endings to the pain center, which will process the information received. It takes some time, albeit very short. He will have time to feel, but he will not understand.
By the way, the brain has no pain receptors, so operations on it are performed without general anesthesia. It is enough to prick the head around the incision site with a local anesthetic, such as novocaine or lidocaine.