1) First of all, the ridicioulous low building speed for some cities. Naturally, well placed cities can make things a lot faster then other cities. The more "hammers" there are around your area, the faster you can build things.
However, food and hammers tend to conflict with eachother. Most of the times, it's hard to get a place with enough food to grow your city to a recent size and enough hammers to build things at a decent rate. Cities that you've placed in areas with a decent amount of hammers will require, even when at a decent size ( for the prehistoric age and classical age, that is ), anywhere from 10 to 60 turns to make normal buildings. Theatres, granaries, you name it. I am aware that building was a lot harder back then, but cities with population numbers that rise above the 100.000's don't need to dedicate themself DIFFERENT CENTURIES at building something. As the time progresses, this becomes less worse, but it still tends to be somewhat awkward.
Its all about balance and specialization- take great care to find the best location for each city, making sure you have a look at what squares will be located in its initial build radius and what square will become available once it grows. Also, since you can now generate entirely different resources from each square its quite easy to completely change a city as it grows.
Specialize your cities so each one has a task, like a factory city or a great person generator.
2) As I've said, cities have to dedicate themselves to one building or unit. Yes, for some reason, you cannot build things simultaniously. You can't even build a building and recruit a unit at the same time. This annoys me a LOT for some reason.
I can just imagine attempting to control multiple build queues in a large number of cities *shudder*
Although I think possibly a separate recruiting and building queue a-la Total War would be interesting...
3) Those AI's are cheating. I'm sure of it. They manage to create a lot of cities AND a large military AND an economy to maintain it. When you wish to create a new city, you have to build a settler, which sucks up all surplus food, thus not allowing your city to grow. However, AI's at the beginning of the game have different cities with population sizes the same as those of cities who didn't build settlers.
There is a set difficulty level (I think its prince) where the AI does not get any advantages, anything higher and it 'cheats' anything lower and you do!
I'm pretty sure the AI has to follow most of the rules, especially in Civ 4 where early expansion can really hamper your mid-game, generally I can keep up with the AI expansion (the trick is to start a few games, run on for about 50 turns, then retire and see if you expand as quickly as the AI does, and just try to find a balance.)
4) The military part of the game is BAD. Although it works with a lot of modifiers so that waging war is "strategic", it still all comes down to the dice which determines a win or loss. The AI seems to have a distinct edge in these dice rolls, and can win victories where you can't.
You know you can see the modifiers before attacking right? Just select your unit and hold it over the enemy, the mods should show up in the bottom left...
I would suggest selecting each of your stacked units in turn and check the modifiers as sometimes they can stack up interestingly and in a way you did not expect, sometimes your strongest unit is not the best...
Also catapults are designed specifically to attack enemy stacks that are two strong, with the loss of a few catapults the collateral damage should weaken the stack until they can be defeated.
Personally I agree that when the odds are in your favour you should ALWAYS win the battle, but take the appropriate damage which in turn will lower your strength.
However I think I have also won just as many against the odds battles as the AI has, its just more annoying when it wins them
5) Turns are way too long. With that, I mean the amount of years they represent. This leads to a number of problems, for example, research is scaled up with these "long turns", and you tend to go through the technology ages quickly. What is bad about this is that a lot of things become obselete WAY too fast. You just made a bunch of longbowmen? Nice, but you'll have to upgrade those in to grenadiers in twenty turns.
Really, the only way they will ever see battle is when you are very close to the enemy and you immediately declare war on them.
When you begin you can decrease the game speed to epic or marathon. These options drastically change the length of the game, marathon slows it down so much that I would actually recommend choosing maps that do not require open ocean travel, as you may be stranded waiting for caravels for thousands of turns!
As for longbowmen being too short-lived I think it really depends if you are at war or not, I always seem to be at peace when longbows come around, so they do seem like they are very short lived- try being at war when they appear! You'd be amazed how useful they are.