Ok, I have three questions, it'd be a great help if you could answer them!
1. Can colonies build settlers and found cities for themselves? I was playing a game on Warlord, archipelago and created a colony on a nearby island, founding Ethiopa, with 2 cities. I left for a while, but they never actually founded any new cities even though there was plenty of room. They did found one new city eventually, but only as i'd gifted them a settler.
2. Is there any downsides/advantages to founding multiple religions? I've founded Judaism, Christianity and Confucianism in my latest game as the Russians, and am now going for Islam.
3. How can I convert to an AI's religion? They haven't spread to any of my cities, and no missionaries have come, and i'm thinking that maybe founding multiple religions wasn't such a good idea, as everyone else is either Buddhist/Hinduism, making diplomacy with most of them quite difficult..
Thank you!
Sisuitil gave you good and correct answers, but would like to expand them a little.
1. You are playing on Warlord level and the AI are slow - they have penalties compared to human players at this level. Could be something else that slowed down the Ethiopians. But usually an AI (even colonized one) will expand to fill the land without any urging from you. BTW,I would not gift a settler, I'd prefer to settle in a good spot and gift the city - because I'm so arrogant I think I can choose city locations better than Zara Yacoub can.
2. AI who found their own religion will eventually adopt that religion as state religion, almost always. More DIFFFERENT AI religions means more AI/AI hatreds (less AI/AI trading and more AI/AI warring, both which benefit you). If you deny them chance to found religions and do not take active role via missionaries to get AI to the religions you want, then you are begging for an AI Love-Fest that you aren't invited to. Can be dangerous.
Religions usually play a very important role in Religious (duh!), Cultural, and to lesser degree Diplomatic victory conditions. If you try for one of these, you need to manage your religions with some thought (not necessarily found one). If you go for Space, Domination, or Conquest... you can always go "no state religion" and ignore their effects entirely.
I found religion(s) when I am trying for Religious VC, or when its the only way to get enough religions for a fast cultural victory (cathedrals!), or as an accidental by-product of taking Code of Laws from Oracle or using Great Scientist to bulb Philosophy. Never worth doing just for the shrine bonuses.
3. You need trade route access with the civ(s) that are using the religion you want. That means Open borders, btw, but not "just" open borders will do (pre-astronomy you can't get spread from a civ requiring Galleons to reach; roads needed before sailing or when no coastal access... rivers, etc). The easiest way is to build a new city with no religion that you do not connect to your own cities, but ihas connectivity access to the target civ. That's not always possible, so a new city right on their borders (as close to the Holy City as possible!!!) will usually do. Then wait. Note, odds of spontaneous religious spread are related to distance from holy city (and doubled if that holy city has the Holy Shrine built). So you should be able to predict which religion it should capture. Also note, spiritual AI tend to send missionaries much more than non-spiritual ones, but you don't need to get the missionary to get the religion spread.
Once you have at least one city with the religion, you can convert to it by going to the religious advisor screen (praying hands icon on upper right) and click on it. Can't do while in anarchy or within 5 turns of a previous conversion. Only the cities that contain your chosen state religion will get any of the religious civics benefits, so you might wish to spread it once you catch it.