1. Early barbarian attacks. I've noticed, both in single and multiplayer with my brother, that somewhere between 2000BC and say 1000AD I tend to get hit by wave after wave of barbarians. Whilst they're no real trouble they do have a habit of damaging my economy by taking out workers and improvements usually before I have a decent amount of troops to spare. Is there some way to protect against this? It's annoying because around that time I'm usually trying to get a couple more cities on the go and put archers in them. (yes I've scouted my immediate area to remove black areas)
1. Build more Warriors.
2. Research Archery early on and build archers for defense.
3. Research Bronze Working/Animal Husbandry, hope you have either Copper or Horses and build Axemen/Chariots for defense.
4. Build the Great Wall (it won't protect your settlers or prevent the barbarians from founding their own cities, though)
5. Fog-bust. Barbarians only spawn in the fog of war, so establish a defensive perimeter of units (2 or 3) around your territory (fortify them on hills/forests). Your units will intercept barbs before they enter your territory and will also prevent barbs from spawning right next to you because of their line of sight. Barbs are stupid and will usually suicide into your fortified units.
Barbs shouldn't be a problem in 1000 AD though

Are you building enough units?
Also, your workers are very important and expensive, especially early on. Don't lose them. Getting pillaged isn't as bad as losing a worker.
2. Workers. What improvements on what tiles? I tend to favour cottages but I usually end up with cities with low hammer yields due to all the forests I've cleared. :S Any tips?
It depends. Specialize your cities. Here's an article:
http://www.civfanatics.com/civ4/strategy/city_specialization.php
3. Units. How the hell does the AI create so many units so fast? And how do they afford the maintenance?
On difficulties above Noble, the AI gets a bonus in everything (research, production, etc.), as well as starting off with more units.
I'll use the ever popular Montezuma as an example. ¬¬ Even though I choose the civs to boost my military production and whatnot, a war with him usually ends up with me razing one or sometimes two of his cities but losing most of my military in the process from his retaliation. He also seems to have an easy time raping my cities with 15 defenders in whereas I struggle to take out a city of his with only two units in, regardless of how many catapults I launch at it.
Hmm, I can't give you precise advice because I don't know your exact situation, but here are a few things to look out for:
1. Did you bring enough units and siege?
2. Are your units outdated? (Swordsmen vs. Longbowmen is not a good idea)
3. Are you attacking with the correct units? (city attack promotions, etc.)
4. Did you bombard the city defense down to 0% before suiciding your siege for collateral damage? (bombarding takes a very long time if the city has walls and a castle)
5. Is the city on a hill?
6. Is it a holy city?
7. Are you attacking a Protective leader?
8. Was Montezuma much stronger than you to begin with? (check the power graph)
If you still have trouble taking a city with two defenders, it might just be bad luck.
4. How come, if I have say a spearman and a macemen in a stack (obviously a stack is bigger but for the sake of example...) and Monte has a horse archer and a jaguar... why when I choose my spearman is he facing the jaguar and not the horse archer (and vice versa). Is there a way to choose which unit to attack or do you always face the most inappropriate unit?
The game automatically selects the best defender in the stack depending on what unit you attack with.
In your example, the best unit to defend against your spearmen is the jaguar, hence the game chose the jaguar as the defender instead of the horse archer.
5. Musketmen. Are these just useless or what? Seems they can't kill anything. Am I wasting my time building these? I always thought gunpowder would be an advantage but they just die so easily.
I'm not a big fan of musketmen either, but they do have two advantages:
1. No ressources required to build them.
2. No good counter in their era.
6. Espionage... Is there a point? I've noticed in the replays that the AI barely increases its rate until 1200AD+, sometimes later. Is there an optimum time to increase this at all?
The best uses for espionage are:
1. Stealing technologies.
2. Causing a city revolt. This is nice because it instantly removes a city's defense bonus (instant 0%) without having to bombard the city with siege. Very useful in war-time and shortens wars considerably.
Direct your espionage points towards the tech leader or your next war target.
Regarding the espionage slider, it is never worth increasing it, with very, very few exceptions, so leave it at 0% and ignore it. Focus on increasing the research slider.
7. Warlike people. If I'm surrounded by say Montezuma, Ghenghis and ummm Alexander or Napolean, even if they are friendly to me, should I just give up? Seems nothing can keep them happy regardless. I had Ghenghis turn on me with a +8 relationship. O_O
Ghenghis isn't much of a backstabber. If he declared at +8 it's because he was bribed, because of an Apostolic Palace vote against you or because your power rating was too low and you looked like a juicy target. Always check the power graph and make sure you have at least 65-70% of the AI's power.
War-like leaders are easy to bribe into wars and are slow techers, so keep them busy fighting between themselves and go after them one at a time with a vengeance once you have more advanced units.
8. The Apolostic (sp?) Palace. The reason why I prefer Warlords to Beyond the Sword. All it seems to do is get me dragged into war. I presume the idea is to be voted leader of this horrific monstrosity? Short of building it myself, is it even possible to become (and stay) leader? >_<
You'll either love or hate the Apostolic Palace

.
I don't have that much experience with it, but try to adopt the AP's religion and avoid being universally hated by everyone by being of a different religion. Building it is a good idea if you can because it guarantees your eligibility as leader in the elections.
9. Money. Where is there never enough money? Even with the shrine it just seems to cost me a fortune in city/troop maintenance. Oh sure courthouses, markets, banks and grocers help, if I can keep Monte off my ass long enough to build them. But it seems that the amount of troops I require to protect my cities, mines, borders and other important resources sucks out any income I get from shrines and cottages.
Gold is less important than research. Gold is useful for mass upgrades and random events, but your top priority should be to increase the research slider with a profit.
If you desperately need gold you can:
1. Sell some old techs to a backwards AI.
2. Drop the research slider to 0% for a few turns.
3. Try getting a Great Merchant and use him for a trade mission.
What am I doing wrong in Noble that worked fine in Warlord?
It could be many things. Not building enough units, wonder addiction, not specializing cities, not expanding enough, expanding too much, not building enough workers, not researching Bronze Working/Animal Husbandry early on, etc.
I suggest you read the articles in the War Academy and read the ALC games (all 24 of them

).