Visible crew/equipment: When Leela runs into Toos' quarters (and finds D84 leaning over Toos), we see a low-angle shot of her entering the room. Look at the brief shots of her before and after D84's line, "Please do not throw hands at me," and you'll see the front of the camera that took that low-angle shot jutting out into the doorway behind her, before it slowly retreats out of vision.
Visible crew/equipment: In episode three, when Toos talks about the disposal of robots, a crewman can be seen behind her, toward the back of the set.
Visible crew/equipment: When Leela bandages Toos' arm, a member of the crew is visible on the edge of the set.
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★