Hi Kimimi, you could just ask me if I'm in-game, but here's a few sites that might help:

This is a JP to EN explanation list for 1.0, but it contains a lot of general useful terms in FF14:
http://ff14wiki.info/?MMORPG%E3%81%A...95%A5%E8%AA%9E

The wiki also lists some of the more common terms under auto-translate here:

http://ff14wiki.info/?%E5%AE%9A%E5%9...BE%9E%E6%9B%B8

As for specific terms:
Limit break is usually abbreviated as "LB" or just written as "リミットブレイク"
Free Company is "FC" or "フリーカンパニー”, usually shorted to "フリカン"
Grand Company is "GC" or "グラカン" for short.
Tank is "盾" (shield), healer is "ヒーラー” or rarely "回復", sometimes you'll just see shouts for "白魔(導師)" which is WHM or "学者" for SCH.
As for DPS, not all JPs are familiar with that term, the most common one is ”アタッカー"

Most of these terms are covered in the first link - if you have any other questions, drop me a tell when I'm not being Error 1017ed.