1.)
So, if I occupy a foreign city, my first step is to burn down their temples. Second: to build a Shrine to one of my gods. I usually keep all other buildings intact, but upgrade every bit of them over time.

Practicing this "strategy" would erase CP if I am right, pelase correct me if I am wrong.

2.)
All in all every foreign building is upgradable with one of your own culture's building, every one of them, save temples. Right?