(1) What is the use of religion?
(2) How do I understand, conceptually, having different religions in different cities?
(3) Technically, what good does it do to my civ having researching different religions? Do they help militarily, politically, culturally or civ growth?
(4) Why would I want to create a missionaries?
(5) If I keep sending missionaries and spread my state religion to other civ's cities, what are the benefits of these missions?
*Question about Uranium
(6) I was in Modern Era now. And Uranium is extremely rare. It fell into Elizabeth territory which is on the far upper left of the map and I was on the far right of the map. Obviously we were separated by other civs. I knocked on Elizabeth's door more than a few times, trying to see if Uranium is up for trade but disappointing enough, it was. Without it, I can produce nuke. How do I get Uranium in this case, apart from seizing the territory which means war against Elizabeth?
(1) Religion gives a

and a

bonus to the city it's in. Religions also allow you to build that religion's temple and monastery. Also, if you have the holy city for the religion (the city the religion was founded in), a Great Prophet can build a shrine in that city, giving you +1

for each city that religion is in.
(2) Each religion gives the same bonuses, and they stack on top of one another. Having one religion as your state religion gives extra bonuses from that religion.
(3) If other civs have the same state religion as you, they'll like you more. However, if they have a different one than you, they'll like you less. If you are using the Organized Religion civic, buildings are created 25% faster in cities with your state religion. With Theocracy, units built in cities with your state religion receive +2 experience points. With Free Religion, you have no state religion, but you still receive +1 extra happiness from each religion in a city, and +10% research.
(4) Missionaries can spread religions, potentially causing other civilzations to switch to your religion. Plus, if you spread the religion which you have the shrine for, you'll receive more

every turn (+1 from every city that religion is in)
(5) That's explained with (4)
(6) You could check and see if any other civs have Uranium, and see if they want to trade it. Or, invade one of those contries with it, and take it.