@Megas Alexandros

That's correct for most circumstances.

To answer # 1 destroying a temple right away is mot the bet solution, especially of it is close to rioting. You don't want to destroy a temple that is giving 30 percent happiness when the happiness is currently 90 percent on low tax rate wich would drop it down to 60 percent risking rioting and revolt. Find other means to raise happiness so when you destroy it you are above 75 percent.

2 most temples aren't upgradable from different factions but therea are some that can be upgraded between differnt factions. Just check first under the tech tree icon and it will show wether or not you can upgrade that temple into your faction.