What happens if the TARDIS (or any of the other Time Lords' TARDISes) lands on a really sloped hill where it's not flat? Would it stay upright or would it fall over?
There's a slight discrepancy between the old series and the 2005 reboot in what would happen to the TARDIS's interior if the TARDIS's exterior is tilted.
As can be seen in the second episode of series 19's Castrolova, when the Fifth Doctor's TARDIS lands tilted the interior tilts with it.
However in NuWho S7: E11, the Eleventh Doctor says
The TARDIS is special. She has her own gravity, I'd explain if I had some charts and a board pen.
when the salvage team step inside of the TARDIS while on its side but find themselves right way up once through the doors. Furthermore, Twelve's TARDIS is horizontal while in Clara's bag during S8: E9 but the Doctor continues to walk around upright while stuck in the TARDIS. He can even "Addams Family" the miniature exterior from horizontal to vertical to escape an oncoming train. However, when the miniature TARDIS falls back onto its side a moment later in the scene the interior does quake although its orientation doesn't change.
Regarding what happens only to the exterior, the TARDIS can fall over if tilted too far, although this may be able to be countered if the Doctor knows the TARDIS won't be materialising upright. In the video @Valorum commented with, the TARDIS can fall if the ground beneath it gives way and it becomes unbalanced. However, in S6: E2 of NuWho the Doctor successfully materialises the TARDIS flush with the vertical face of a building, indicating that it doesn't have to fall from a tilted surface if it is known to be materialising onto one.
The TARDIS would likely fall over, as it has before
While not exactly the situation you described, the Third Doctor serial "The Curse of Peladon" has the TARDIS land on a mountain slope where it begins rocking, going to about a 30 degree angle. Shortly afterwards, some high winds pick up and it falls over, off the mountain (but being indestructible, it remains intact).
Note that in this case, the TARDIS materialized without issue and the Doctor noted that it was a "smooth landing". It's unclear what would happen if it tried to materialize at, say a 60 degree angle, but I suspect the Doctor wouldn't report a "smooth landing".