With the vanilla game, if you opponent has the token, coins given to opponnent instead of giving back to the bank?
Only coins being paid for resources (wood/stone/clay/paper/glass) are given to your opponent. Some buildings directly cost coin and you pay the coin costs directly to the bank, regardless of whether your opponent has economy or not.
Will the coins you pay to activate divinity treated as constructed a building/wonder?
No, the costs you pay are as you said, for a divinity and not resources (wood/stone/clay/paper/glass). Also, Economy does not affect Engineering.