"I think they have found plenty of cases where people weren't legally dead before they removed parts."If you are referring to "removing parts" for transplantation, please give us a factual example with documentation.
"They do have to take the organs immediately after life signs extinquish?"
Not true in most western nations where brain death is the criteria for death. Donor organs can be kept viable long after the brain is dead. Perhaps you are referring to those areas of the world where cessation of a heartbeat is the definition of death. Waiting until there is no cardiac function does make organ donation very difficult.
"I realy don't trust hospitals, if money is involve"
"Hospitals" do not make decisions about when death occurs.