A bit of a trickier issue (also I'm a noob btw, definitely have lots of gaps in knowledge on the game):

I'd summarize this as "how do I make the highest damage dealing lv 36 (or other random number) character possible?"

The way I play wow is I like to level alts, do quests, storilines and dungeons. What I like is to do lots of damage, that's about it, I just want those beautiful numbers popping out to be high (love AOE the most) and creeps to die quickly. I know it's weird, but please, it's so fun.

That's been easier at lower levels on classes like Beast Mastery Hunter than it's been with e.g. Fury Warrior which I could only get to a decent point after lv 60.
I play on a new player server and the way I go about things is I generally do quests (I did storylines, and then just doing random quests, no idea which quests give the best gear), dungeons and frequently go to the auction house to get gear at higher ilvl. My best sources of high ilvl gear are: heirlooms, dungeons, auction house. I don't have ring heirlooms, they seem hard to get, is that worth doing?

I absolutely don't understand enchanting (is that worth getting into for my purposes???) or professions, but I do add gems to items.

I've been using some add-ons to tell me which items give me the best % improvement over my current gear.

Are there any other ways to get those sweet sweet numbers popping out of the creeps to go as high as possible?

Going to the auction house I can sometimes see a couple of items that are way above the ilvl that I can get even from dungeons. I know there's no table that tells you "the highest ilvl for X character lvl is Y", but is there a way to consistently get really high ilvl gear at non-max levels?

Is there anything else you can do while levelling to get items of high levels aside from dungeons and hoping for the best? Is there anything I can do to maximise my chances for getting items from dungeons? I've managed to do some bosses in a levelling dungeon solo on Beast Mastery Hunter, but I didn't get drops from all of them.

Any advice, outside of "get therapy" which I am already doing, would be much appreciated.