(...) However, I was killed (maybe overkilled) by overexpansion - I always keep captured cities even in Bts and my monetary balance was slowly sliding to negative vallues. I expected this, fed my war machine by pillaging and rampaged on. However, as I eradicated the Grigori, i had yearly income cca -30gp, about 12 cities and no research. My units went on strike. (...)
I'm surprised you're getting inflation problems at Warlord level. What is the sequence of the first several techs that you researched?
I used to play a lot at Warlord level and didn't have too much trouble with inflation control. I moved up to Prince, which is lots tougher in this respect.
You might want to try the following: avoid games where you start in the middle of a heavily forested area (don't even bother starting with jungle). Try to get Calendar & Festivals as early as possible. Depending on available resources, Plantations can help finance a civ's early expansion. Markets are a
must when building your second or third city. After you get these two techs,
then go for Bronze Working (otherwise you're at risk of getting victimized of course!)
Look at your civics too -- by the time you build three or more cities you should have at least God King in place. As soon as you start capturing cities away from your capital be ready to switch to City States. In addition to that, use the cheapest civics you can get. Watch your finance screen (too many units can be expensive, which is why planning for great city production too early in the game can come back to haunt you!)
There aren't a whole lot of ways to make money in FfH. You got to manage techs and civics very carefully. Check your cities' specialists to maximize what you need -- one city for production, one for science, and one for... money! I hate to do this, but once in a while, you might have to switch one or more cities to generating only gold to avoid bankruptcy and strikes. If you have two good production cities, you might want to consider specializing one as an exclusive military center (leaving the other to build non-military wonders perhaps).
Here's a example of tech a research sequence that might work (opinions are welcome since everyone has their own preferences/experience):
Initially: Agriculture, Crafting (as appropriate to your civ)
1. Exploration
2. Calendar
3. Mining (or before Exploration if you have lots of unwooded hills and no good Plantation sites)
4. Festivals (try to time this one with your 2nd city)
5. Bronze Working (time to beat up a neighbor!)
6. Beeline toward a religion (you need Monuments and God King by now; Temples of Kilmorph also generate a good supply of cash)
7. Education (for City States)
After that... your game events and strategy should dictate what happens next, I would think.
