First, is there any actual tutorial for this game?

Secondly, I'm wondering if its possible to take over a city and keep its race, given that it "would be in anarchy except for your troops"?

IIRC Wizard's Throne had a kind of tutorial in the first campaign map, but not Shadow Magic.

Yes, you can in principle keep any race.
Your race relations are not dependent on the race of your Wizard, but on the composition of the population in your empire. So if you conquer enough cities of a particular race and that race becomes the dominant one, they will be happy.
So you need to make some long term goals about which race(s) will for the backbone of your armies and which cities need to be either kept in check by troops or migrated to a different race.

Yes, bit THE alignement of tour wizard also playes a role.
Hahahaha! iPad autocorrect.

The halfling campaign is the tutorial, and the game has some excellent tooltips, but if you need more info the manual is here.

Some city structures (e.g. temples) increase happiness, and in most cases that's enough to prevent riots, altough sometimes you'll need to leave some troops behind (wich should be there for defense purposes anyway, leaving a city unguarded is one of the worst ideas you can have in this game).

Generally speaking, in a normal playthrough you'll rarely have to worry about morale - unless your wizard has the "Anarchist" trait, or you're trying to deal with pure good and pure evil races. If you do, consider researching the "Peace Keeper" trait (20+ rep with all races) but note that it's mutually exclusive with "Conqueror" (+50% exp gained in combat).

Building the shrine of order greatly increases your city's happiness/morale, making them less likely to revolt. But that doesn't mean you can take that race's troops out to fight. As soon as they leave the city, they might desert you, and even turn on you or join your enemy. To keep races that don't usually like you with your traveling war party, you'll need to choose the bard ability for one of your heroes per group. That's a very strong ability and can make even very reluctant troops stick around for at least a good long while.

It doesn't always work, though. That's why, for instance, a not uncommon quest reward, the golden dragon, can be useless at best. If you're an evil race even with a bard in your group, it is sooner or later going to break ranks and fly away or turn around and challenge you.

I'm trying to remember if Bard's Skills stacks. I think it actually did in AoW1, but I'm not sure about Aow2/SM. Probably not.

Edit: Looks like it did stack in AoW1. Also, a unit's Bards's Skills would only effect other units in the stack, not the unit itself. So you'd need 2 units with Bard's Skills anyway so they could increase each other's morale.

This is SM.

I'm curious, it *seems* like an evil party is ok with being under the command of a good player, as long as you don't try mixing it? Has anyone else found this or was I doing something that I didn't realise

I think the composition within the party (and the relative strengths) affects morale the most. So even if you're a good player (ie empire is mostly good races) you might still get away with for instance a full orc party. At least if you haven't razed/migrated any orc cities lately. I wouldn't try a pure evil party though.
Or maybe you had the peace keeper skill and that's why it worked.

Edit: I tend to stay within the alignment of my chosen race (or one step away), so I don't get to do much morale experimenting. Currently playing nautral and including a chaplain and a draconian elder in a mixed party makes karaghs and even vampires happy.