I was just wondering how would religion differ from culture? would they interact and influence each other?
can the player pick a state religion? does a religion convert the whole city or a single population point at a time? do they spread naturally without you actively pushing it?

I was just wondering how would religion differ from culture?

Your borders aren't set on religion. Religion seems to be more of a flavor to add to the game.

would they interact and influence each other?
Yes, You'll be able to see other civ's cities with the same religion, and i believe they are also slightly more friendly towares you.

can the player pick a state religion?
yup.

does a religion convert the whole city or a single population point at a time?

I believe it was by population, would make more sense. Although i think if there is no religion in a city, the whole city converts....

do they spread naturally without you actively pushing it?
Yes over time, they would slowly convert to your religion, and vice-versa.