Does anyone else do this?

[Viking]

After you've already taken a city is there any way to exterminate the population? Maybe leave and wait for them to revolt but is there an easy way to do it?

Take out the garrison in that city, gift it away to an enemy, re-occupy it and exterminate.

Is that true? I've always wondered about tearing buildings down, especially their temples that I can't upgrade

Replacing a building from a different culture wit one from your own reduces culture penalty with 5%(more if there`s very few buildings in that settlement), if you upgrade the settlement you will remove something like 20-30%. I haven`t tested upgrading out good enough to give you a clear answer.