1. Dont worry too much about aether currents early on. Half of the zones for the expack the story takes two seperate visits to cover, so you wont be able to get the spots from the second half(or quest related currents from the second half) until you return. You can get all the currents from
Ruby Sea, Azim Steppe and The Lochs
on the first trip though, if you want(you probly do). With that said, it never hurts to ping the aether compass a few times while moving from point a to point b - you can get a few of them out of the way while doing other tasks.

2. Depends a little on what you have. I had mostly upgraded shire gear, and was taking the on-class rewards by level 64. They werent all better then what i had, but i started giving the extras to my retainer to get her gear level up. But i also only play one class, so the quests that didnt have a reward i could actually use i tried a mix of materia and gear to try and sell on the board. Some of those made me good money, some of them were utterly worthless because everyone else did the same. With that said, the defensive values in particular are taking a giant step upwards over these 10 levels, so you definitely dont want to try to stretch level 60 gear the whole way. Bonus though, the leveling dungeons from the expack drop(straight to inventory) one guaranteed piece of gear for the class you came in as, so each clear you get at least 1 new piece(and it wont drop something you already have, so potentially several new pieces - one exception is you cant force weapon drops this way).

3. Dont worry about nearby hunts. You need a TON of allied seals to buy speed upgrades, but there are only(currently) 6 speed upgrades to be purchased with centurio seals. SB hunts give centurio seals(and tomes presumably if your level is high enough), but they dont reward any allied seals. And even if youre getting your hands on tomes early, the vendor to spend them at doesnt appear until you complete a certain quest toward the end of the storyline. Having some to spend as soon as you can is nice, but the verities dont take all that long to farm up(creations are a different matter because of their capped status).