Hello! I'm in love! But a few Questions...

[Anova]

- Am I able to "reduce my level" and go explore areas I have outleveled?

There will be level syncs available for any instanced content and the real-time events called FATEs. Otherwise, you will be able to visit most places on the map at any time.

- Where can I purchase a mount? And for that matter, how much gil is considered an average amount? At level 15 I have about 5,000 gil.

The chocobo mount becomes available after a Lv.20 story quest, My Little Chocobo. This quest becomes available after you join one of 3 grand companies. These grand companies are akin to player factions and are used to delineate sides in the upcoming Frontlines battleground patch, Defenders of Eorzea. There is no big difference between them and you are able to change your grand company, although it will require some work to do so.

To buy your chocobo, it will cost you 2000 company seals (token currency earned by doing FATEs, grand company hunting logs, and grand company leves). In general, you will be able to earn enough (or close to) by unlocking and completing the Lv.20 dungeon, Hatalati. It will fulfill a number of hunting log entries and the dungeon itself gives seals.

- Any lingo or abbreviations or whatnot that are common in FFXIV I may need to know?

This is a fairly comprehensive lexicon for your reference.