I play on challenging:

1. Do you feel monsters act too randomly? Yes sometimes, but less often in the last patch.

2. Do you feel like early game monsters are too powerful? No, the only problem is with the danger level (sometimes strong monster are weaker than weak one and vice-versa, so I think can be difficult for a new player to evalute correctly the enemies)

3. Do you feel like the Faction AI is getting a free pass with monsters? Yes and No, but I think it depend more on point one then other things.

4. Do you often lose cities from wandering monsters? Never happened in the last patch, rarely in beta5, very often in the beta4... I saw that if you leave a garrison in a city (even a weak one), the monsters tend to leave alone the city.
So, I don't know if the "solving" is related to the patch or to a change in my gameplay.

5. Does losing a city cause you to quit playing? It depend from the season: in the beginning Yes of course, after No (it depend also from the number of cities and importance of the lost city)

1.  Monsters do seem pretty inconsistent with regards to when they attack your stuff, which makes it hard to plan strategy.  It feels like consistent aggressiveness would work better.

2.  It feels like high-danger monsters should be further away from your starting area, yes.

3.  The AI factions do seem to face less monster attacks - which adds a significant annoyance when you take an AI city and have to choose between clearing out the monsters or risk losing it to a random wandering monster that wasn't cleared out.

4-5.  I reload and powerlevel my heroes enough that I've only faced inevitable city loss in 1 or 2 early-game scenarios with a Strong+ attacking army randomly hitting my city - I usually resort to teleporting them away via cheats in that case.

FYI, I used to play on expert, and now play on ridiculous.

Where's my graph and chart as promised by the OP?

Okay okay. I just wanted to make sure I had most of the responses before I made the chart. Be up soon.

No. The point is to see whether or not the monsters and factions are acceptable from all levels of difficulty. There are not enough beta testers to divide the chart by difficulty and so we must assume that things are scaling well. So far it looks like an overall positive opinion about monsters. I thought people hated them alot more than this. And we are expected to get non-simultaneous turns in the next update. I think the chart will show that no metascore points are likely to be lost from monster issues.

Wait, are the monsters aggressive?

Sincerely
~ Kongdej

1. Do you feel monsters act too randomly?

 Randomly? perhaps. i've seen them sit and do nothing at times when my army walks right next to them, get a threat then nothing happens. and then at times when suddenly their hole is in my control area they begin to wander around aimlessly away from my territory.

2. Do you feel like early game monsters are too powerful?

 Yes! the new spell coals or whichever it was caused my entire army to die after 2 turns. decimated my heroes.

3. Do you feel like the Faction AI is getting a free pass with monsters?

 I've only seen the AI fight the monsters once. but for the most part it seems the monsters avoid the AI players. or the AI avoids them, either way they don't seem to interact at all. at least that i have seen.

4. Do you often lose cities from wandering monsters?

 I've lost 3 cities to wandering monsters. i find it rediculous that you can't take it back, let alone there is no ruins or anything to mark where your city fell.

5. Does losing a city cause you to quit playing?

when early in the game it does. having my only other city being conquered and my heroes decimated and sent home injured caused me to rage quit.

1. mostly yes.

2. yes (under the current circumstances) and no (in general).

3. yes

4. yes

5. yes

Detailed answers:

1. Do you feel monsters act too randomly? - Yes for monsters with lairs which are woken up. They should (try to) destroy whoever was disturbing them and then go back to where they came from. But random behaviour is absolutely okay for wandering monsters.

2. Do you feel like early game monsters are too powerful? - As long as dragons woken up by AI players enjoy burning my towns: yes. The key point is that the AI should play by the same rules as the human player. As long as this is the case, I have no problems with strong early game monsters.

3. Do you feel like the Faction AI is getting a free pass with monsters? - yes, definitely.

4. Do you often lose cities from wandering monsters? - yes, definitely.

5. Does losing a city cause you to quit playing? - yes. After a large number of reloads (on "easy" difficulty!), I quit playing FE totally and hope for a new version. The current built is more frustration tolerance training then fun.

Currently, FE is definitely not recommendable.

Here's your pony.

I haven't really said anything for FE but this issue has completely prevented me from enjoying the beta.

1. Yes - No apparent rhyme or reason to any given group's activity

2. No - Not until lairs spawn upgraded stacks do they become an issue

3. Yes - Strong+ stacks routinely cross the world, passing every AI city along the way, seemingly hunting down and razing my least defended cities (not that defense matters, nobody is killing dragons and shrill lords when the most advanced military tech in the world by far is spears and leather armor)

4. Yes - Constantly, and never from a stack that I 'freed', since I don't build next to them for that very reason.

5. Yes - Immediately. Maybe I am a bad sport, but permanently losing one of my centers of production, regardless of its size, and never being able to replace it, is a game-wrecking experience, especially if I am in no reasonable position to prevent it in the first place and it happens seemingly at random.

I am not fundamentally opposed to the idea of lair-based or wandering stacks wrecking my cities, but the current system seems terrible. A few alternatives that would make it infinitely more bearable:
A) Instead of automatically razing the city, destroy some of its buildings and population proportional to stack strength.
Have lairs exert an area of influence based on strength (1-3 tiles) that either prevent cities from being founded there and/or send out routine patrols within to burn any structures (outposts, free buildings) and slay any units in the area
C) Always have a disturbed stack beeline for the nearest outpost or city to attack it instead of leaving the target open (read: crossing the world to attack the human player)

Any of these would be preferable to the current system. There is also option D) Just stop monsters from attacking cities period. Let them harass my armies, my pioneers, my outposts, my free-standing buildings, but not my cities. Cities are almost like characters in the Elemental world, if I wanted to play a game where my vital characters die off horribly and randomly and cause me much weeping and gnashing of teeth, I'd play XCOM. Actually, I'm going to do that now, I think.