based on the rules, im pretty sure Tak's Athlete ability is a passive bonus you can use whenever applicable
about the ability symbols, i dont know, but i notice that Athlete and Gust dont consume any resources, but Gale Strike uses 1 surge. i think youre right about combat vs noncombat abilities.
the little dot is easy to explain: it's whether or not you used it. when you use Gust, mark the dot; and then unmark it and the beginning of each page. when you use gale strike, mark the dot next to surge; and unmark it at the beginning of each page.