If my tooth is chipping and rotting and pieces falling out is nerve dead ?

Not necessarily: There may be extensive decay, but it may not be deep enough to cause the nerve to have died. See your dentist for x-rays, an examination, and a repair.

Not necessarily: But very likely. Have your dentist evaluate it for restoration or extraction.

Depends: If the decay is near or into the pulp, the tooth may have to have a root canal, regardless. Extraction is the alternative. See a dentist asap!