I have few more questions:
Which wonders are the most important?
It would be easier to answer if you had asked "what wonders are the least important?". I can give you some examples there: The Shwegadon Paya, The Hagia Sophia, The Sistine Chapel, Chichen Itza and others.
Now, this is to be taken with a grain of salt because any of these wonders might be very beneficial to your game, it is just much less likely the case than if we were talking about The Oracle, for example.
The Sistine Chapel is almost useless unless you are going for a cultural victory or your borders are under severe cultural pressure and you are running many specialists all over the place anyway.
The Oracle is NEVER useless because it gives you a (possibly very expensive) tech for free.
The Great Lighthouse can range from close to worthless (if you have almost no coastal cities) to super-powerful (if you are on an Islands map).
I could go on like that but if you follow sample games in these forums and look at your own games you will find out by yourself which wonders are good, and which are not so good. Sometimes it's not obvious to a beginning player if a wonder is really good because its value might depend on a certain strategy (or map type). This is why I recommend to read sample games and see what the experienced player do with wonders, and why.
How do i balance building like granary building and military building?
Granaries are good because they greatly increase the rate at which your cities grow, and growth/food is probably the most important factor to your overall success. There are not many reasons a city should be without a granary for a long time, and thusly they should be among the first buildings you construct in a new city.
Barracks increase your power rating just by building them, so its never bad to have many of them because a high power rating intimidates the AI and makes them less likely to attack or threaten you. Apart from that it's good to have them in your production cities for the obvious reason that you will build your units there ;-). The further specialized military buildings should only go into cities where you plan to build many units, usually your best production cities.
There is absolutely no rule to how to "balance" buildings because it entirely depends on your overall strategy to the game at hand.
How much should my cultural bar be if i want to achieve cultural victory?
Again, this can't be answered in a straight fashion, but usually you want to have it at 100% at some point of the game to generate as much culture as possible per turn. When to set it to 100% depends on when you have researched all the technologies you need for self-defense and cultural buildings.
Why do some corporations actually take money away from my cities?
Because they would be too powerful if they were free. In fact, ALL CORPORATIONS take away (a lot) of money from your cities, but if you own the headquarters ("holy city") of a corporation you can get back some of that money, or even run a profit.
How do i break alliances between AI if they are really friendly to each other?
The best way to do this is to bribe one of the two into a different religion, which means you have to spread it first. That can be costly and time-consuming. If they are both peace-loving and sharing a state religion it is practically the only way though.
Sometimes there is no practical way to break close AI alliances so you just have to put up with it.
How do I prevent slave revolts?
By not running the Slavery civic at all. There's no other way to avoid them.
What's state and non-state religion?
Your state religion is the one you converted to in the religious advisor screen (and indicated by the symbol on the score board). You can have no state religion at all, too.
I believe they're only in BtS
