Is it possible to be staying awake for wisdom teeth removal?

Yes, you can: It is not mandatory that you be put to sleep for the extraction. But since all extractions are not the same, allow the surgeon treating you to help guide you in making the proper decision.

Very common: The appropriate anesthesia depends on the complexity of the dental treatment and your own comfort zone. With the profound local anesthesia and IV sedation you will have no recall of the events of the dental treatment or experience any pain. In your case IV sedation is recommended. Best of luck.

Yes: Yes. if you can have it done with local anesthesia, it is considered safer than general anesthesia or other type of sedations.