Usually one question per question. I'll answer the temperature one.
Unless you were very close to the poles, and not too deep, it would be shirt-sleeves livable with or without a power source. Maybe not exactly comfortable, but people would not be dropping dead of cold as long as they had a light jacket.
Scroll down this article to item 12 and you will see that Carlsbad Cavern is a very modest 56°F year round. In Mammoth cave this article tells us it stays around 54°F. Closer to the poles the temperature will be lower.
This Wikipedia article explains how temperature varies with depth. It's complicated by location near various things like volcanoes and plate boundaries. But as a back-of-the-envelope calculation we have the following.
Away from tectonic plate boundaries, it is about 25–30 °C/km (72-87 °F/mi) of depth near the surface in most of the world.
So probably you would be more worried about not being too deep when the power goes off, because your cooling would stop. If you were, say, 3 km deep, you'd be getting pretty close to boiling without some A/C working.