So I thought I'd see how poorly I'm doing in the game. Floor 3, Level 5, going up against corridors of flanking spiders that like to just come out of the shadows from behind, the sides, etc.
Note this is my FIRST PLAYTHROUGH, and I have not been looking up ANYTHING so far outside how to make spells. Only really looked for tips today, outside dexterity is evasion, not damage. So paths are set, whether they're optimal or not. Looking for where to go from here.

Minotaur Fighter:
Going axes and light protection. Put a couple points in Athletics to start.
Human Fighter:
Swords and heavy protection, heavy armor at minimum. Also a few stray points in Athletics.
Lizard Rogue:
Mostly dodge right now with some in missiles. Probably going missiles after hearing throwing sucks in one of the guides. True or false, because I'm just not seeing bows, and the only missile weapon uses rocks. And I want to keep my rocks. Mostly spams shurikens and knives.
Human Mage:
Got the first spell in each school at least, plus some in Spellcraft and defense.

Minotaur Fighter: This would probably have been your better option for heavy armor due to the increased carrying capacity from high strength - which, unfortunately, isn't very effective as a melee stat.

Human Fighter: Nothing really wrong here.

Lizard Rogue: I suspect that you'll have cranked Dexterity, but that's actually a nigh-useless stat for ranged characters, because ranged weapons never miss - strength is THE stat for them because it boosts damage. Otherwise though, archery vs thrown is mainly a style preference. They're about equal in terms of overall output.

Human Mage: Unfortunately, mages don't work very well when spread thin - the general pattern is to race to 10 or 18 spellcraft and then head as deep into one type of magic as you can. The strongest spells of a school generally require 20-30 points, and you don't have many more than that by the time you reach the end of the game.

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One of the unstated effects of attack skills is that they also passively boost your accuracy and damage with the related type of weapon by +3 per 4 points in the skill, which dwarfs the benefit of the stated stat boosts in various skills.

That said, you can still get through the game with a relatively unoptimal party, but it's best to focus on one primary combat skill per character, since you'll only get around 48 per character from level-ups and a spare 20 points (total, not per-character) from certain treasures (if you find them).

Can you go Mage-less in this game? Because I'm really not figuring out how spell-casting works... at all.

You can, although having mages is pretty useful. But, in the scenario you can't figure them out, the game doesn't become impossible even if you don't use them. Have a backrow of rogues who can still fight no problem: the other one for example can have the skill which let's you attack just like you were in the front row (forgot what it's called: assassination maybe?), and the other may use bows or throw stuff. They shouldn't be identical characters however, because both of them would be using weapons from the same weapon class, and therefor compete against each other. Make your characters unique.

Thanks, I'm actually going with 1 mage because I did figure it out. Though I made the mistake of using all of her initial skill points in spellcraft, rendering her pretty much useless. However, now I have her with an ice skill so it works well.