You surely will only access to a dragon by Quest. A difficult and long chain of quests, actually.
They will surely provide some kind of boost to Prestige to all the cities ("Hey, we have an all mighty dragon in our side! Yay!") and/or bonus to diplomacy ("Sorry for being late to the negotiations table, I''s making aure that the accomodations for my dragon ally were good enough.")
It'd not be impossible to get more than one dragon. But there won't be easy mode for that, only Terminus Hardcore Mode.
There might be male and female dragons. And there might be some mating involved in the game. Dragons as mounts for your army won't be in the game. If you can have one for your Sovereign or one hero, you will feel happy. And we are supposing that the dragon is in a good mood and allows you to use him/her as mount.
For mods, anything goes. For campaign/pure-Elemental, I'd not hold my breath.
If by ability you mean quests, yeah. Skills per se, it seems doubtfull unless dragons become common like a Burger King. To purchase a skill just to increase slightly your chances to recruit a uber unit (a single one... maybe two... don't let your hopes to fly too high there; in huge maps could be some more, I suppose) doesn't seem a worthy invesment. Specially when that uber unit won't win the game by itself (hopefully).
Answered in "the official spirit" of past threads/posts about the same topic.