My games are no more combat heavy than any 'normal' D&D game.. About 50/50. I personally believe that a character should be able to handle itself in both Roleplaying AND combat. Otherwise he/she is going to find theirself standing back watching half the game.
if you want an example of how I tend to run games (Specifically Epic ones), I've got two Epic Games running on the boards right now.. One's evil, one's good:
Prevention
Return to Power
They're both about 200 posts long, but if you can wade from beginning to end, I think you'll like it.
And just a side note... the last tournaments winner was a Prince. Allarion Sarutobi of Lyrevan, and he's one of the best roleplayed characters I've ever seen, which is half of why he won (He managed to talk a few people into surrendering to him, which is worth 3 kills a piece.. And I don't mean through Bluff/Diplomacy/Intimidate, but rather through excellent roleplaying. He WAS a very god fighter, though, on top of that.
(Though I'm not telling anyone what happened in the castle or afterwards.
One thing to keep in mind though... if your character isn't a powerful fighter, then why & How did he get invited/brought/accepted into the Tournament?
Also, is the concept specifically SUPPOSED to be non-combatant, or is that a side effect of you not usually making powerful/Epic characters? If it is the latter, there are many here who would be happy to help you with a few tips/pointers.
to your Other questions: No spell like abilities over 4th level either.
As for LA/HD, it depends on what you want. Just ask. I'd prefer no Liches, or anything else that's inherently 'unkillable' except by very specific means.
Vampires, however, are perfectly acceptable.

I can tell you right now that there's going to be about a half dozen of them in the tourney.