Conquest RankingsFollow

Yes. You keep the airpass. You become rank1 in your new city. And all of your outpost teleports get cleared. (at least they were for me). You still get the rewards for attaining rank in your new hometown (i.e., gil for attaining each new rank).

If you switch back to your old city, you regain the old rank, have access to the CP you gained with that city (you don't have access to these when you switch), and have to redo the outpost teleports yet again.

This was my experience, as i went Bastok -> Rank5 -> Windy -> Rank5 -> Bastok -> Rank 6.

Have fun. The story line is definitely different. It's also interesting to see it unfold after you've been playing for a while and have more points of reference. ^^