Crown cuttin can be done by giving local anesthesia?

YES. The "crown cuttin" the preparation of the tooth for the crown is done under local analgesia.
Yes. If your talking about a craniotomy. Yes it can. Sometimes the surgeon needs the patient to answer questions dying the surgery. An anesthesiologist is present to sedate the patient during parts of the surgery.
It depends. Depending on which crowns are being worked on, a local anesthetic may be all you need. Discuss this with your dentist as sedation may also be available.