Most of your questions don't have just one answer, it really depends how you want to play the game and what type of victory you're going for. When going for a culture victory, how you play and what civ to play as will be very different than when going for a domination victory. That said, here are some answers:
As in all Civ games, getting up the tech tree as fast as possible is the best way to pull ahead of other civs. In order to do that, you need to build the tech buildings (library, public school, etc.) as fast as possible and have as much population in your cities as possible. Prioritizing the research that will get you to the tech buildings is a good strategy.
It is almost universally acknowledged that the Tradition social tree is the best of the 3 starting ones. I like the 1st Honor policy for the early culture boost, but better players seem to skip it. Once Rationalism unlocks, the policies there that boost your tech are must have. I like the first couple Patronage policies that help increase and maintain your CS influence. Some people like the Piety tree.
You need siege weapons to wear down a city until one of your melee units can take it. Unfortunately, siege weapons aren't very useful for anything except taking cities, but cities are very hard to take without one. I try to have 3 siege units before I attack a city.
I never, ever conquer city states. You can't destroy them, you can only capture them or liberate them. Keeping them as allies gets you lots of nice things and is essential for a diplomacy victory. Conquering them earns you a big warmonger penalty so the other AI civs will hate you.
Keep a close eye on your happiness and your gold. You really don't want either going negative.
Hope that helped some. Oh, and BNW really adds to the game.
