"Does wearing a wig kill your remaining hair off? I know it gets hot and sweaty under the wig so that leads to more hair loss. "

No, it doesn't. There is no study that shows getting hot & sweaty leads to hair loss.
Losing your hair is genetic.

You only use a hairpiece where you've lost or are losing your hair anyway.
This is usually on top with the back & sides remaining unaffected.

Its hard to impress on someone who hasn't felt (in their hands or on their head) how light and airy a hairpiece is.
I promise you, its not like wearing a hat at all.