What is the highest displayed damage you can get without temporary buffs?
Probably in the 180-200 range as a Trilling on Naga City (only level with enough gold to truly fuel its full potential). Actually, you might be able to push it even higher by going human and using the keg of health to fuel the reflex boon. Maybe 220-240 might be the highest.
Highest max health?
It'd be interesting to see what it is now. I know I hit 300 with Orc Rogues using old absolution, but now that it's gone I'm not sure how high you could really push it.
I do often hit the 200-mark every so often as a non-dwarf, so 300 is probably still feasible if you don't care about actually winning.
Highest max mana?
Best I've reached is the low 40's. Eight conversions as an elf (+8), three hits of boost mana (+9), Elven Boots (+3), Mage Plate (+5), Pendent of Mana (+2), and you're in spell-spammer heaven. At that point, however, pushing things much higher becomes nearly impossible. There are no more +mana items to grab, and that many mana boosts will preclude a detour through the GG's religion for enlightenment. You'll be very hard pressed to get more than two or three more points than this. I think 45 may be the realistic maximum possible.
Forget about winning the dungeon or building a viable character. Just pick a category and distort the game as hard as you can around a single mechanic. Floor us with your 200+ damage trisword wielding orc rogues of Dracul +Glowing Guardian+Taurog.
Tikki Tooki is the way to go, and with this much base attack you definitely want human over orc. Also, a character that focuses on nothing but maximizing damage is
actually quite playable in this game, so winning probably wouldn't be a huge issue at that point.