What stats do mobs have at each dungeon level

After the first floor, I generally just pray whenever I see the statue - the quest is either going to be trivial (ie, go find an item or put this item with the shrine) or hard (kill this special monster or an army of regular monsters) and the difficulty of the quest doesn't change much with respect to how long you've been on a floor.

On the first floor, I might take a few character levels first, as you'll likely gain several levels just exploring the floor, and levels are relatively cheap. When you stop being beaten half to death by every bat and blob that shows up, you'll know you're ready.

Even if you clear the whole level like Oak suggests, monsters will slowly respawn. The random nature of the quest, coupled with the random nature of the floor, and the random nature of the game in general, mean that things can go from very good to very bad extremely quickly, with or without the quest.

I'd focus on glitching, trapping, or debuffing the AI (ie, sticking them in a spot where they can't get to you, fighting near a Glyph/door, or rooting them in place) to give your hero a bit longer to mash on them before they can do damage to you.

And remember, Dying is Fun!

There are no longer any negative effects for using a weapon that you are unskilled with, except that you will not get the benefits from your weapon skill. It used to be that you got a debuff from using a weapon without that weapon's skill, similar to the debuff for dual wielding without the proper skill, but that was removed in an earlier update.

I have actually begun not choosing any weapon skill, as it allows me to choose another useful skill, and I find that the bonus of being able to use any weapon without having to worry about losing skills more than outweighs the loss of bonuses from the weapon skill.