The hero intelligence question warrants a more detailed response, but in a nutshell - they are REALLY DUMB, and needs work. It's especially highlighted with the monsters, because I haven't put in too many mechanics around them yet.
What the current logic comes down to is basically a dice roll based on only limited inputs, with actions taken once the hero feels comfortable with his outfit. They also only ever attack monsters under the terms of a contract, at the minute.
In the future there should be a few more routes for heroes to attack monsters:
1) 'Goody two shoes' people from the Church, and adventurous Swashbucklers should go for it, for kicks or out of righteousness..
2) The mayor should start crapping his pants and take out a contract on the monsters, opening up a route for the more selfish characters.
3) I would like more conditions, which aren't anywhere near implemented, such as Summoners with a 'Capture Soul' scroll or something, attempt to go and ... capture their soul ...
Presently, they only attack monsters accidentally if they appear in the shop with them and interrupt their browsing.
What conditions are there currently for a dungeon leveling up? Is it related to hero death count, or the number of monsters? Or something entirely different?
Just hero kills at the minute. They need something like 4 level 1 heroes to advance a level (or 1 level 4 hero). This goes up to 8 equivalent to get from level 2 to level 3.
I also have trouble starting, should I just buy as much as I can or put up contracts?
Contracts are pretty risky, but can pay off well if you are lucky.
It might be worth bearing in mind that you can normally get away with selling things at 120% of their base value. As long as stock keeps moving, you should be able to generally make at least 20% on it (not always true, depending on whether you get the item for a decent price in the first place).
Also keep an eye on heroes 'shopping' and see what they are shopping for. Are they missing one of weapon/clothing/armor? If they are chances are you just need one of those in stock and if its fairly priced the hero will snap it up. You can get a quick turnaround on stuff by nipping over to the Barbarians or the Fighters to buy something in (lower level shops are more likely to price things a bit low, generally speaking). and hopefully quickly flip it for a profit.
Also if you try and keep plenty of stock in, it maximises the chances of a visiting merchant cleaning you out and giving you a good payday.
And yeah, try and examine those things you win from the auction house. It's possible to get, say, a 'summon lost soul' scroll which can shift to the right hands for up to 120 bucks ...