Do you have to have a general anaesthetic to have impacted wisdom teeth taken out?

No, it's optional: Wisdom teeth removal do not require general anesthesia, however the experience my be more comforttable with a milder IV sedation. Local anesthetic is required in either case. In other words, the dentist will numb your mouth so you won't feel any pain. But, if you don't want to hear the possible sounds of cracking, drilling or feeling strong pressure, it's more comfortable to be lightly sedated.

Probably not: Most of those are still amenable for extraction under local anesthesia, although, a dentist would be the one to decide on that.

No: There are several options for the removal of any tooth including local anesthesia, nitrous oxide analgesia with local, IV sedation and general anesthesia. Your best option should be discussed with your oral surgeon.