Plot hole: Azmael doesn't recognise the regenerated Doctor (In the shape of Colin Baker) whereas on most other occasions other Time Lords do recognize each other through telepathy. This is odd behaviour by Azmael, considering that Azmael and the Doctor HAVE actually met before, and possibly more than once. (Azmael last met the Doctor in the Doctor's fourth incarnation, and was the best teacher the Doctor ever had. On that occasion, Azmael got drunk.).
Plot hole: Peri makes no mention of the Doctor's heroic sacrifice on her behalf, nor thanks him for it (no wonder he's touchy).
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 ★