There's an easy answer to both of those - the black hole is a supermassive and has a very sizeable accretion disk made primarily of star material that is being slowly sucked into the hole - and that material is still actively putting out light and heat. Lots of it. The accretion disk was easily observable in the film.Originally posted by Feruk
Two obvious ones come to mind (not spoilers as it's in the preview):
1) If the planets go around a black hole instead of a star, why is there daylight?
2) Black holes emit x-rays, not heat. How can there be liquid water on a planet?