How can you tell if they're dead or alive?
Can you freeze them? If you can, do you freeze them on the half shell or keep both shells on?
When I have opened a raw clam that was bad/dead--it smelled terribly. I have never had a bad/dead oyster luckily. No, you cannot freeze oysters in the shell unless you mean for one hour to make them easier to open.
If you can't pry them open, your oysters are still alive. I suppose you could freeze them, but you would definitely kill them if you did. If you froze them on the half-shell, they would not be very palatable once thawed.
Frozen Oysters are commercially available, both in the shell, half shell, and out of the shell.
Those out of the shell are frozen with liquid.
Frozen, prepared Oysters Rockefellar are commercially available.