some questions about how religion spread

[Pumabear]

Religion sometimes spread automatically between cities. I wonder if it will spread faster if I make it my state religion?

And if I make a religion my state religion, will religions that are not my state religion spread slower?

 

[Gumbolt]

Don't think your religion matters in terms of Religions spreading. Unless you have a civic that stops other religions spreading. Or your city already has another religion.

Best way for religions to spread is by open borders with AI. This allows missionaries to enter your land.
Also by being connected by road and sea. Religions often spread to cities nearby. Religions can only naturally spread to other cities with no religion. Sailing is important if you want sea trade network.

Overall I wouldn't base your entire game on the probability of a religion spreading. Monuments and libraries are most guaranteed way to get culture. That or build a misisonary yourself to spread the religion.

I am sure someone will correct me if I have this wrong.