What you want is power. Not strength. Power is simply the amount of force(strength) over time, which would be speed.
You want power in your legs in kick boxing...not just strength. In squats or leg presses, drive the weights as fast as you can (no bouncing, please!) from a static position to a final position. You don't simply move the weights methodically, you drive it! And since kickboxing is cardio, everything is done in higher reps with lots of drive to it. Add volume training to it but watch out for the over-training since you are doing kickboxing as well. You'll need more rest and recuperation from doing a combination of exercises (ie kickboxing plus weight training).
As for the rest of your questions, you are not clear on exactly what your goals are.