OK....

1. Cult Centres are the City-States that have the symbols of one of the religions next to their name. White symbols denote good religions, green denote neutral and red evil. While it's not mandatory, I recommend that if you have a choice, you should select from the alignment you plan to play under most circulstances. For instance, if you plan to play your civ as a Good civ and you have met 3 "aligned" City-States, one devoted to Torm, Waukeen and Cyric each - go with Torm. Religious policies can give you boosts from having followers of the same alignment as you, and each pilgrimage or quest completed awards two followers of that city-state's faith.

They also have small circles with five-pointed stars underneath them to indicate that they're ready to receive a pilgrimage/give out a quest. To do either of those, get your hero to within two spaces of the city-state itself. Don't worry about diplomatic penalties - heroes never incur them, and can freely go where they wish.

2. It's VERY uncommon to go more than ~50 turns without meeting other civs, except MAYBE on island maps. I'd recommend more exploring :)