You have a sort of pseudo-autojump in RIK. If you jump and keep holding jump, you will automatically jump once you land as long as you're landing on something that's HIGHER than where you jumped from!
You're required to use the "pseudo-autojump" for doublejumps to work. It's also extremely useful for stairs. Naturally it also works on ramps and alike.
There is no need to do "quick" jump clicks in RIK. Unlike Q3/Defrag, there are no bad effects from holding jump while in the air. It will not affect your speed or acceleration in any way.
Halfjumps are simply a "weak" jump that gives you less height. To do one, hold SPECIAL (per default hold the right mouse button) as you jump. You can never do two halfjumps in a row. After you do a halfjump, you will lose the ability to halfjump until you've jumped off a surface on a different height level. Rampjumps, walljumps, and so on counts for this and will give you a "new halfjump" you can use.