I'm having a cyst removed from the side of my nose. Will I have a local or general anesthetic? Can I eat on the day?

The type of anesthesia used to remove a cyst on the side of the nose would primarily be determined by the surgeon performing the procedure.  You should contact the surgeon who will be removing your cyst to find out the type of anesthesia that will be used.  This will determine when you could eat surrounding the procedure.  If the cyst is fairly small, I would think that it could most likely be removed just with local anesthesia.