I am God. (Religion and it's game changing effect)
Founding a religion is an amazing buff, no matter what type of win your going for.
The AI goes pretty strongly towards religion so you have to prioritize it and that means for most civs taking the time to research and then build shrines as soon as possible.
I prioritize two Great Prophets at first to get the religion fully created.
Spreading your religion with Great Prophets in towns with no religion doesn't seem to be a good strategy, use GP's when you want to clean up a town with more than one religion and missionaries for spreading to towns.
33/66 faster spread vs longer range. I would suggest always going for longer range it seems to spread religion much better than the speedup.
Putting an inquisitor in your Holy City prevents AI civs from bombing your religion. Inq active ability only work on your towns, you can't clean up CS/Friendly cities only the GP can do that.
Missionaries dies inside other civs border in four turns, unless you have an open border agreement with them. The GP has no issue. Both Mis and GP can enter lands without open border, since Missionaries has four moves it is possible to get to a town before it dies, but the way it dies means it loss 25% strength pr turn it's inside the civ land, so I doubt it's worth it except in very early game with low pop cities.
Going for faith like desert or tundra as pantheon works very well in cutting down the faith buildings/citystates you need early to compete with the AI's.
Many religion "buffs" is period restricted, like you can build wonders faster in the two first periods or buy military units with faith.
Late game you can buy Great People with faith if you pick the appropriate social policy, just need to open the policy to start buying. A Darius player could spam buy artists by picking freedom and saving up faith pre-industrial age.
That thing about stationing an inquisitor in your holy city, do they reduce spread passively just by being present or is it really just an intimidation thing where the AI realizes it'd be a waste to use the missionary there?
The parked inq just disable the use of Greater Prophet/Missionaries, if your religion is weak, you could still get some conversion due to natural spread.
That is one thing I haven't figured out though if 2 or more religions is hitting a city, will the one with the highest pressure convert the low pressure religion?
I think that situation requires an Inq/GP to clean out the other religions.
I have to say i agree: playing a game of Faith is a game changer in Gods & Kings.
Some of the new civs introduced in the expansion are religious: Celts, Maya, Ethiopia.
The way faith and religion is a game changer is for example take Korea: build faith to be able to purchase GPs in the industrial era to create special improvements. Faith can help with any sort of victory...there isn't a reason to think it's particularly catered for cultural wins.
I think it really tosses up the existing strategies as per the Handbooks: