Yes. You can have a wisdom tooth removed with only local anesthesia. Some patients choose to have the procedure performed without any type of analgesia (nitrous oxide) or other types of sedation or anesthesia.
Usually. They numb the area with an injection of local anesthetic. Laughing gas (nitrous oxide) may be used as well. A general is usually not necessary.
Yes. Many single tooth extractions, are done with a local anesthesia (numbing), though nitrous or IV sedation anesthesia are certainly options.