Behind that rabbit.
Or when he’s telling what he knows about physics concepts that don’t translate well into human.
The row of vertical cylinders with sliding doors that the Doctor goes into. It’s a Tardis parking lot.
We don’t know that’s what it looks like with its chameleon circuit turned off - that might be what it looks like when the circuit is set to “museum display.” 
Anyway, my point was about interiors, not exteriors.
I love the round things!
What are the round things?
For all the talk about Star Trek, Gallifrey really does seem to point towards what happens if you combine a completely post-scarcity society with a Prime Directive that is actually mostly enforced.
Nothing is actually needed, so you end up with the mentality of a HOA in control of the most powerful technology in the universe, who doesn’t use it at all, and turns a usual blind eye to the one person who does use it for good, unless they need him as either a hero or a scapegoat.
With “this kind of thing” basically referring to the Whoverse version of Stephen King’s Langoliers. Except they only come when you make a temporal paradox. Apparently the Time Lords would have fixed the paradoxes before.
[someone had a better memory than I]
Couple of points:
The TARDIS first shows signs of sentience in a very early First Doctor episode with Ian, Barbara, and Susan. The Doctor takes it more or less in stride (and is the one who figures out what’s happening), but it’s clear that he didn’t know about this aspect of TARDISes and is surprised by it.
While the TARDIS frequently has a swimming pool (currently in the library) it doesn’t always. The Sixth Doctor mentions jettisoning it due to its leaking. In one episode (Logopolis or Castrovala, I think) the Fourth or Fifth Doctor jettisons something like 40% of the interior space of the TARDIS to provide extra thrust. That seems to imply that the interior isn’t infinite after all, but doesn’t necessarily: if the rooms were all finite and equally sized and number sequentially, they could jettison half of them by eliminating the even numbered rooms, and still have an infinite number of rooms (and infinite space) left.
I don’t think it’s necessarily infinite as much as it’s unbounded. Like Gay Deceiver after visiting Oz.*
- Sorry, so sorry
“Stretched”? :dubious: 
The closest thing the TARDIS has to a point is that flashing light on the top.