Well, for the first question, Alchemy is actually one of the branches of magic that are dying down, Alchemists are almost gone and the few that remain have joined what you'd call the 'science side' and helped develop the Kaijutsins, in other words, artificial mages. In terms of it, Alchemy is the study of the very essence of magic, and it also studies all of its applications. In this RP, alchemists won't be so much as 'fighters', more like 'savants'.

Ki users are, most basically (as explained by Haruna), like the characters in Hunter x Hunter. Since I haven't seen the anime, I'll just give a little info on what I know after reading the wiki. Basically, they can use their Ki to engulf parts of their body in that same element, and fight using them, as well as 'throwing' it from their palms (projection), so basically, yes, kinda like benders, just a little more restricted to the fact of using it most often in your own body.

I knew Jelly wouldn't explain that through, xD. Don't worry, I'll give you the full version. First difference is the fact that they are 'created' not born with the gift of magic, to do this, right after they are born they are implanted with an special kind of implant (This implant is completely safe, as it has shown no signs of rejection by the human body.) that allows them to use Renkai, the form of mana in this RP for Kaijutsins, if you'd call it something. This implant is also the only way to pilot the mechas, as it is necessary to imprint the info the implant gathers as it grows along its holder. Also, through the modification of this implant, Kaijutsins become more powerful, without an actual need of training, but this kind of experiment is not also dangerous, it is also illegal. 

Hope that answers your questions, if it still isn't clear, just say so. :P