A: You cannot teleport the Teleport Chamber itself. We should probably word the card just a tad bit clearer to specify any other Keeper.
Note that the Transporter in Star Trek Fluxxen has a different function than the Teleporter in Star Fluxx, however. Rather than moving a Keeper from one player to another on the table, it takes any Keeper on the table up into the hand of the player who has the Transporter. Again, you can’t use the Transporter to transport itself up to your hand. We’re not sure why you’d want to, but we thought we’d answer that just in case.
Now, if you’re mixing more than one Star Trek deck, there will be many Transporters in the deck, and it’s quite possible that someone might want to use one Transporter to suck up another Transporter to their hand to take it away from someone else. Unfortunately, we’re going to have to rule that out on the basis that it would definitely cause some sort of terrible Transporter-related disaster, probably involving stray tachyons or chroniton particles.