im pretty sure the fog doesnt have a chrome bezel inside it like the headlights do that you can paint. more likely youll have to go to overlay route unless you want to tint the outside with some spray like people do for the tails and side markers
yes.. it will reduce light output.... but if you want to "black them out" you have no other option. Like reut1 said, there is no bezel to paint inside the fog
I have rock blocker film on my fogs and I can tell you it is not as easily reversible as it seems. to correctly paint them, it is going to cost some money. to paint with off the shelf stuff, it should cost about 20 bucks.
either way is about the same. if you paint them, prep them correctly and use an adhesion promoter. otherwise, you are just wasting your time.