Organ Donation in Halacha Is it an obligation, a prohibition, or a choice?

Donating organs from a live donor
From a dead donor posthumously
What are the types of organ retrieval after death?
Is there a nafka Mina between them in Halacha?
If a frum Jew decides to donate organs after death, is there anything different they should requests than the general public?
Are you allowed to sign the back of your license to become a donor?
If someone donates an organ against Halacha are you allowed to be a recipient of that organ?