Is there some sort of auction house in the game?
There's a market ward. It's an instanced area and you want see it on the map. In Limsa it's north of the Aether plaza. You want to go to the Uldahn Mercantile Area and do a search there for lower gear.

If there isnt an AH, where do lower levels get gear?
At your level it would be worth it to gather/buy mats and make your gear yourself.

Do you get gear from quests and how often should i be upgrading gear while leveling.
There are some miniquests that give you items and gear. You can get gear from leves. You can also get gear from dungeons like Shposhae which is east of Limsa (for level 15ish gear) or from TotoRak (Level 30 gear). You can get higher level gear from Lower NMs also.

how often should i be upgrading gear while leveling.
It depends on how fast you're leveling and what content you're doing. I upgraded gear every 10-12 levels back in the day.

Do different venders in the game sell things at different prices?
Nope

When im looking at gear from a vender it has a "optimal level". whats that mean?
It doesn't mean anything. Wear it if you find it useful and your character can equip it.