1. Do you feel monsters act too randomly? As a general rule, yes. I don't mind wolves and mites wandering around aimlessly, as they're expected to be stupid and weak. However, it doesn't make sense for a Fell Dragon to be pushed out of his home by a handful of defenseless settlers, and then wander halfway around the world to raise hell for an empire that had nothing to do with his eviction. Instead, he should make a nice pioneer souffle and go back to his cave to nap until the next group of settlers foolishly tries to take the fertile soil next to his cave. This is the kind of behavior that would be expected of a dragon, and having them behave nothing like expected is confusing and makes players believe the AI is somehow cheating.
2. Do you feel like early game monsters are too powerful? Not really, as long as their behavior is predictable. I think that there's a pretty good balance between early game monsters that even a solo sovereign can take out and end-game monsters that will destroy you. The problem is their behavior is too simple, which makes it seem random and unfair to the player. To use the above example, if I find X'thi'lioth the Fell Dragon ten tiles away from me, my knowledge of how dragons operate says that any city whose zone of control hits his cave is going to die, whether it's my city or the AI's. However, if I'm understanding Frogboy correctly, monster AI doesn't even know what a city IS, let alone how to make a beeline for one and eat it so it can remain undisturbed. This makes for extremely counterintuitive monster AI behavior, and makes strong monsters seem even stronger.
3. Do you feel like the Faction AI is getting a free pass with monsters? Not really. I think there are still some kinks to be worked out with the simultaneous turns (I did once see a Krax army and a Storm Dragon hanging out on the same tile, but that was the only wonky behavior I've seen thus far), but other than that the AI does seem to have a tougher time with monsters than I do, judging by the number of injuries their champions take before any wars break out.
4. Do you often lose cities from wandering monsters? Rarely, but when I do it's infuriating. I've noticed that since .982, wildlands monsters are much more aggressive about leaving their territory, which sucks because I like having lots of wildlands to run around and conquer. Sometimes it's not a problem; I don't mind seeing a lone shadow warg early game, because I can actually take care of it. But when a hoarder spider and its army are threatening my only city at turn 13 (yes, this happened), I'm likely to ctrl-N or just quit for a little while.
5. Does losing a city cause you to quit playing? I just reload to a point where I can prevent that city from being lost. Usually the most recent autosave is enough for me to put a tremor on the baddy until my champion's army can show up.