Is it possible to take body parts and attach them to another body?

Yes to an extent: We are pretty limited so far but, if you think, that is what transplants are. We can do internal body parts fairly well such as kidney, heart, lung, pancreas, cornea. Skin & tendons are body parts too but i suspect you are thinking of attaching a thumb or a foot & we are not there yet as such would take attaching many nerve and blood vessels. Face transplant has occurred; the process is similar.

Yes and no!: Transplantation as it is called require a good tissue match..Otherwise the body rejects the mismatched parts. So the only way to attach a part is under the cover of immunosuppressive drugs which have to be taken for a long time..May be even life long. This is being done increasingly and body parts are being successfully tranplanted in more and more cases every year. But it is not an easy process..