Waiting for the GCD for Aero I is just something you'll have to get used to. Aero II has a cast time, so that won't feel the same when you get it, but you can have II and I active at the same time, so you'll still be casting I and waiting it out.

Exp chains are completely different from skill combos. You get an Exp chain on any combat class when you kill monsters equal to or greater than your level within a certain time limit (which shows under your Exp bar). Skill combos are available for melee classes (and not MNK; MNK skills function similarly to combos, but they aren't strictly combos like GLA, MRD, and LNC get). Mages and archers get other ability bonuses instead. For example, once you get Freecure, using Cure I gives a 15% chance to make your next Cure II within 15 seconds free.