Some Questions HELP!!!!

[Veteranewbie]

I am trying to play regent in a peaceful way (i can beat regent 1v1 if i just mass warriors and rush AI) but i never able to success. The AI expands/build military/build wonders/tech so fast, it eventually strangles me with better technology, larger army and larger empire. I wish somebody can help me in it.
Here are some questions i wanna ask:
1. What is the ideal expansion speed? If i expand too quickly i always find that it taks ages for my city to grow big, and if i expand too slow i will get beaten by AI in military and culture.
2. How to trade fairly with AI? Even in Chieftain level when apparently i have a much larger military (i got about 10 ICBM in my cities, and have marines/tanks etc. which are killing off the remaining indians) and I wanna sign a protection pact with russians they are greedy enough to ask for at least 20 gold/turn (They are polite to me.) Also when i wanna trade for world map the AI always offer me their world map and wants my world map with somethg else (but when i make it a deal i see that their world map is about the size of their territory map).
3. Infrastructure......... do i need to build all of the buildings avialable in all cities, is it good or if i dont what else should i build?
4. Why the hack is the battle so unfair? How the hell can a regular caravel beat my veteran battleship? How can a freaking regular spearman beat my elite marine? (Both are full health)

 

[Aggie]

I am not going to reply on all your questions, because others may have answers on all of them, I don't.
However, you can start with the war academy

 

[Phantom Lord]

1. The growing speed of cities depends mostly on terrain and government. Use builders, builders, builders and go for monarchy early. Cities with enough food supply can grow faster than they can produce builders / settlers. If a city reaches its population limit, it's a good idea to let it produce builders from time to time.

2. They AI usually has many units, but not neccessarily many modern units. Concerning trade, well, you have to pay the price they want or you can wait. Technologies become cheaper the more civs know them.

3. Build what you need ... depending on your plan for the game, how do you want to win?

4. Have a look at this.

 

[KillerSheep]

3. Building choices are different for every game, but there are some basic building rules that seem to work out well (at least for me they do)

- Don't build more than you absolutely need in cities isolated from the rest of your empire. For example in a city on a faraway island only used to gain some resource build only a temple, barracks, harbor, walls and troops. Other improvements are useless as the city is probably too faraway for commerce due to corruption etc.
- Be sure to build walls, barracks and lots of troops in towns situated on small strokes of land, and so blocking entrances to the continents. As this is something the AI usually not too happy about, it can lead to the AI declare war and battering your chokepoint towns with loads of troops.
- Be sure to build temples in every town before anything else