Insulation in basement ceiling

[Daniel Fisher]

I am doing a rehab to flip on a house that has insulation in the basement ceiling. Some of it is missing and what is there is upside down. As in: the paper is turned down rather than towards the heated area.

Would you replace the insulation or just remove it and leave it uninsulated?

If you would just remove it, would you paint the ceiling? The house was built in the 1940s and has rough cut joists that are darkened with age. And what about wiring and plumbing? Would you just paint over everything?