A few general noob questions.

[Dutch_guy]

1. Occupy, enslave, exterminate - what exactly do each do, why should I do them, and when?

If you take a city and are low on money then extermination is your best bet. Enslaving the populace will send about half (?) of the current population to other cities who have a governor in them, you also plunder some of the cities riches - but don't get as much money as you would if you exterminate. When you occupy the city you don't deport the populace, nor do you kill them. You get a modest amount of loot and keep the current Population.

So, you should exterminate if the city is simply too big (i.e. you fear the squalor penalties) or if you need the cash. Or if you fear you can't hold the city and don't wish to give the enemy a large tax-base back.

You enslave if you need the population directed to other core (governed) cities - who then might be able to upgrade to a higher level of city.

You occupy if you don't want the populace to suffer needlesly and like the idea of being able to tax the lot of 'em. As you know, more people equals more tax revenue. Generally it's smart to occupy low populated cities (otherwise you might wait a decade to finally upgrade the city) or even cities of the same culture as you.

2. Why does some of my heavy cavalry just charge and then fall back. Is it meant to be like that? It's extremely annoying when I'm trying to cut down routing warbands.

They do that, why is not really known. Although it might be because certain members of the unit are lagging behind the main bulk of the unit - which confuses the persuing AI. To circumvent this problem, you should simply order your heavy cav. to move (run) to a position in front of the routing unit. They will cut down the routing unit if they move through it.

3. Which units get to do the turtle shell manuever thing? I can't wait!

Only late Roman Legionares have that ability, and only in Rome total War (not in Barbarian invasion). So you're going to have to wait until the Marian Reforms before you can use the Turtle formation.

4. Can someone point me to advanced diplomacy tactics? I want to really force someone to give me half their lands and half their treasury while I grin menacingly.

Well the diplomacy isn't exactly good in this game, however there is a certain exploit which allows you to rip off the AI. What you do is send them your Map Information, The AI loves to have it (why is a mystery) and 'll pay insane amounts of money to get it. When I say insane, I mean it. Ask them 10K and they'll do it. Experiment with asking more, you won't be disappointed. IIRC, in some patch, this exploit was addressed, which patch made it impossible I don't really know.

Other than that exploit, you should check the Diplomacy guide, stickied right here in the Colosseum[1].

Hope that helped!

[1], apparently it isn't here anymore, however this is where you can find it