Electrical problems

It's kind of hard to understand your question. If your engine is running hot, do you continue to drive it until it cuts off? If so, this will blow your engine. You need to have your cooling system checked out.

As for your lights, what do you mean they died? Did your entire electrical system die? And after new battery, was it OK? How do you know your oil sending unit is bad? And if there's any check engine lights on, you should have the computer scanned.