Yes, I've used a friend's bleed kit to bleed my Elixir CR's and it worked perfectly. Shouldn't be any different for the Elixir R's as they're pretty much the same design.

Yes you can use this kit with the Elixir 5 brakes.

This will work with the Juicy 3 brakes, however you will need to flush the system of DOT 4 fluid first and then replace it with the dot 5.1 fluid.

Unfortunately this bleed kit will not work with Promax brakes

I have the same issue with my Tektro Auriga disc brakes, seems we don't stock a compatible bleed kit at this time but I think the issue is due to air getting into the fluid so it just needs a good bleed and service. I removed my rear wheel and pushed the pistons back out with a screw driver, put the wheel back in and pulled the lever then repeated the process and this did help a little.

YouTube seems to be the best possible resource for technical information, you can actually see the job being done too which helps a lot with the technique of the job and the tools involved.