[@Archmage MC] good question, i'll try and answer as best i can!

the various powers are inherent to the dragons (i'm working on a list of premade breeds and their abilities as we type, actually!). the riders do not gain these powers, but they can direct their bonded dragons telepathically on when to use them. that's not to say the dragons are slaves to their riders' will—they retain their autonomy, it's just that they're devoted to their partners (and vice versa) and tend to listen to what they say. non-bonded humans can order/ask a dragon to do something, but in that case, the dragon is much less likely to respond. 

in some cases, a dragon can temporarily extend a power to their rider, but this takes focus, energy, and [i]trust[/i]—for instance, a sea dragon can temporarily give their rider the power to breathe underwater, as long as the dragon isn't too badly injured or unconscious. however, this does not work for the majority of offensive powers—i.e., a thunder dragonrider isn't going to suddenly gain the ability to shoot lightning from their hands. (i'll pseudoexplain this by saying human physiology can't sustain the Overwhelming Power of dragon abilities for long.) over time, though, you can start to see the effects of long-term partnership; while that rider can't shoot lightning, they might give a static shock to anyone who touches them, or maybe they always know when a storm is coming.

tl;dr: dragonriders stay human, except in a few special, temporary cases, but their dragon will do things for them using their powers. hope that helped!