No there is not an episode which explains his fear of heights. Probably because it's a fairly common phobia and most phobias are not caused by an actual experience, but more from a psychological fear or mindset.
its been his dream since the start. he probably will become hokage ( maybe now anytime soon though). He has shown much progress if you think about it. From shadow clone to resenshurikien. So he probably will become hokage, possibly 7th or 8th.
Yes. At least I think so.