A: If you are using the Teleporter in Star Fluxx, then yes. Whatever Creeper or Creepers are attached to the Keeper teleported will move as well. That’s one of the ways you can get rid of Creepers in front of you: to teleport the Keeper they’re attached to to some other player.
Note that the Transporter in Star Trek Fluxxen has a different function, 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. In those cases, it’s more like a repeatable, personal Beam-Us-Up-with-Transporter. In those cases, think of it this way: both cards get sucked up into the hand of the person with the Transporter, and then the Creeper, which can’t be held in your hand, goes back onto the table in front of the person who took the Keeper.