Yes, dead lobsters can be cooked. If you are cooking several lobsters and some are live and some dead, to distinguish between the two you can put a rubber band on the claw of the dead/live lobsters. When they are cooked, examine the meat in the tail. It should be firm and not soft in order to be eaten. www.sagamorelobster.com/instructions.php#dead
Yes. lobster is killed in the cooking process or you need to kill the for cooking. But is is better if they are still alive to have it fresh. Make sure that the lobster isn't dead for a long period of time.