1. What should I be researching first? The world has a ton of mobs and the AI can be aggressive. Should I always go for warfare first?
I tend to go warfare for the first three techs - get logistics and then weapons up to ranged (until you get longbows). Design a unit with nothing but a longbow and train up parties of them, they're pretty effective in city defence against most early game opponents and they're cheap. I'll also tap the diplomacy tree as soon as I'm ready to build my second city to grab trade so I can set up a caravan route between them. The extra gold and food is nice, and the road lets you pull in defenders from your established city to assist if the new city is threatened.
2. Should I build every building in each city or should cities be specialized?
Specialise. The economy boost buildings only affect resources connected to the city, so you're wasting your time building a granary if the city has no attached farms. I find for best results specialise in either arcane research, tech research or gildar production to make full use of the level up bonuses, prioritise those buildings and then max out any farm or mines before worrying about another speciality.
3. How quickly should I be expanding? If it's a fast expansion, how do you defend so many cities?
Depends on the map. Remember that unlike civ or MoM, the natural income from a city is pathetic. Therefore only build cities where you can exploit some resource. Again, gold or research is my priority, but if I'm in need of some other resource like iron or crystals I'll found a city where it can only access those, though I won't grow it beyond level 2.
4. When is the right time to marry off one of your kids?
Personally I use them primarily for diplomatic boosts.
5. With weapons being so expensive, how do you boost the stats of your champions?
Adventure can bring in nice items, but particularly gold and XP. Also some research in the magic tree unlocks various magic items with stat enhancing properties, and the enchanted armour is ridiculously cheap and the best I've seen so far in the game.
6. What are the best ways to increase your gildars? I find the weapons/armor are expensive. Building stacks of soldiers are expensive. How do you get the money to cover these expenses?
Gold mines and specialised gold focused cities will bring in anywhere from 30 - 60 gildar per turn. Adventuring can also fill the coffers - once you can explore level 2 sites you'll get a lot of goodie huts which give you 200 gildar simply for walking over them.