Yeah what do you do when other Civs ask you to help them but they want a rare valuable tech that only you have? I've been denying them but they always get mad at me and then put all their trading options in red text. Is this a case of darned if you do, darned if you don't?
More or less. When a civ asks you for something, and you give it to them, it makes them like you, but then they also get what you gave them. When you deny them, it keeps them from getting what they asked for, but they get upset. Trade-off either way, you just have to decide which is more important, and whether your relations can stand a small hit.
In Civ 3 you could always see the mood of your citizens when you zoomed to the city. I don't see this in 4. Is there a way to see who's happy and who's not? Does the city riot if it's not happy?
No, there's no more rioting or civil disorder. It's all on a citizen-by-citizen basis now. When someone in a city is unhappy, they still eat but you get no work out of them, so it's something you want to avoid.
You can see what their mood is, just mouse over the happy/unhappy faces at the top of the city screen, and it will tell you how many points of each you have and why. As long as your happy points equal or exceed your unhappy points, you get no unhappy people.
Maintanance and health. My capital has grown to about a level 15 and it's not very healthy. I have built a granery. What else can I do to improve health?
The following things improve health (not including difficulty level):
1) Where you build your city. Having it by fresh water gives you a +2. Forests give you a plus depending on how many there are. Flood plains and jungles give you a minus depending on how many there are (but flood plains are good for other reasons).
2) Food resources. These can be hooked up to your road network just like resources in Civ III. They include: rice, wheat, and corn/maize; sheep, pig, and cow; deer and banana; fish, clams, and crab. Each of these supplies one healthy point, more with certain buildings.
3) Buildings. Some buildings give you bonuses for food resources or certain luxury resources in your network. Others just give a health bonus, period. I suggest looking up buildings in the Civilopedia.
4) Civics. The civic Environmentalism (requires Medicine) gives you +6 health in all cities. (It has some minuses, too, though, so study it before choosing it.)
Does it matter where your city is located from the capital in Civ4? As in does health decreace and maintenance become more expensive the farther away it is?
Maintenance yes, health no.
Specialized Cities: I'm still not sure how to go about this. What type of terrain should make me decide to dedicate on city to only one type of building specialization? For example I have a city that is producing plenty of commerce, food, and hammers. It's not as much commerce as some other cities but it's still in the upper echelon. What should I devote this city to?
As a general rule, your top commerce city should be dedicated to commerce, your top hammer-churner to major production, and your top food generator should be set up as a Great People farm. Note that the first two refer to cities OTHER THAN your capital, which is very often both the top industrial city AND the top commerce city. (It's rarely the top farming town, though.)
Some commerce terrain is also good for production, e.g. gold, silver, and gem mines. Other commerce terrain isn't, e.g. seafood resource squares and flood plains with cottages. Because of those precious mines, your top commerce city may not totally suck production-wise; there's nothing wrong with that, because you'll still want to build some buildings in it. But it's unlikely to be your best (or even second-best) production city. And you still want to dedicate it to commerce. Other cities that are less obvious can go either way, it just depends on how much specialization you want.
Only thing is, the cpu doesn't always highlight the one I like most. Why is this?
Because you need to question what you like most, I think.
There are multiple things you can do with a worker in any given terrain. For example, given the right tech, a hill could have a mine on it, or a windmill. A mine will give it extra production, while a windmill will churn out some food and commerce. (More of each with certain techs and civics.) Which is better? Depends on what the city needs most. A flood plain, grassland, or plains square gives you even more options. You can build a farm on it (+1 food, +2 with Biology), or a cottage (+ commerce -- a LOT of commerce once it grows to Town size), or a workshop (+ production, - food). If it's on a river, you can also build a watermill (+ production). Which is best? Again, depends on what the city needs.
Speaking of Wonders, why shouldn't I build as many as I can? In the game I'm playing now (my first game ever; it's on default settings), I can pretty much build what ever I want and get it done pretty quick. No other civ is even close to me.
Sounds to me like you must be on a pretty easy difficulty. The answer to your question is that as you raise the difficulty, all that becomes harder and you have to pick and choose which wonders to build.
How can I get other civs to want to trade their valuable techs with me? (Get them from red to white text.)
Get them to like you better. Change your state religion to the same as theirs, or give them something for free, or go to war with their enemies. When their opinion of you goes to "cautious" or better, they'll usually trade. (Except Tokugawa. He's just a jerk.)
Early expansion: Why is this said to be a crippler? It seems to me that the reason I got ahead so fast was because I built alot of settlers and expanded early on. Also in Civ 3 this was the key to the game. How is it any different in Civ 4?
Because in Civ4, you have maintenance costs based on the number of cities and how far they are from your capital. There is no longer maintenance costs for buildings, but there is for each city, no matter how big it is or how much it contributes (or doesn't) to your budget. In Civ3, you could build a city and the only cost would be the corruption to its commerce and production, and that would never go into the negative (until you built something that required maintenance, of course -- and that would often take forever at one hammer per turn). In Civ4, you can build a city and it will actually COST you money, not just give you next to nothing. On the plus side, though, there is no longer any hammer waste or corruption as such, so you can build just as fast in a town producing 20 hammers per turn in the far reaches of your empire as you can in one next door to the capital. But that far town is likely to cost you some money and be a net drain on your treasury.
Religoun: How do I use the missionaries and what effects does religoun have with neighboring Civilizations?
Missionaries of a particular religion can be produced in any city with a Monastery for that religion, or in any city that plain has the religion in it under the Organized Religion civic. (It does not have to be your state religion for this.) A missionary is a unit. Move it to a city that does not have the missionary's religion, and you will have the option to try to spread the religion to that city. Note that if it's a foreign city, you will need an Open Borders agreement or else a missionary entering the foreign territory is an act of war like any other unit. The success in spreading the religion isn't automatic. It's harder the more religions are already in the town. Succeed or fail, your missionary disappears. If it succeeds, you'll see the little icon for that religion join the others already there, and get the message "Somethingism has spread in Podunk."
What it does:
1) If it's your city, and either the religion is your state religion or you are under Free Religion, having the religion in the city gives you +1 happiness. It also allows you to build religious buildings for that religion. (Note that you can have multiple Temples, for example, each of which gives you +1 happiness. Religious buildings also let you have citizens become Priest specialists.)
2) If it's a foreign city, there is a chance that the other civ may convert to your state religion if that religion is present. If it's not, he not only won't but can't. The more of his cities have your state religion, the more likely it is he'll convert. I've done this, tried to get someone to convert on the diplomacy screen, seen it in red type, closed the screen in frustration, and then had him convert spontaneously on the very next turn. When you have the same state religion as someone else, you get a very significant diplomatic bonus. When you have a different state religion, you get an equally significant penalty.
3) If you have the Holy City for that religion (place it was founded) and have built (or captured) the Shrine for it (it has to be built by a Great Prophet), then you get +1 gold for each city in the world where that religion is present.