I'm 5'9(yes short), how tall should a low box be for me, and also a high box??
It's all relative to what's parallel for you. It's very dependent on how wide your stance is, and how thick your butt is. Most of your training should be 1/2-1" below. A low box would be 2-3" below, and a high box would be 2-3" above.
What Wild_Iron said. Also, if you are very inflexible in the hips, what works well is to progressively work down to that height. Get a bunch (4-6ish) of 1/2 inch mats or something and put them on a box that's at depth for you. From that high box, you can work your way down week by week until you are hitting depth comfortably.
floor should be the height for a box squat
12 to 14 inches
Haha, sounds simple, but a decent way to go about it is to find something around the house that puts you at about parallel when you sit on it (no weight or anything), and measure that.
You'll want to keep that number in mind and use a box about an inch lower than the object for regular, few inches lower for low box, and higher for high box.
It's a good reference point and you can do it at your leisure outside of the gym, no reason to screw around with actual boxes/mats/etc. (whatever you're using).
That's dumb. Do you even know what a box squat is?
It completely depends on your shin height. If you hip flexibility is at least adequate, you should use a tape measure and find a height where the tops of your knees are at or slightly higher than the top crease of your hip.
One very important factor to remember is that a box squat is not the exact same movement as the free squat. This is especially true when using an athletic stance/olympic stance. At the bottom of the box squat, your shins/knees should not move forewards at all. In some cases they actually go behind the knees. This sounds odd but if you keep in mind that the box squat is primarily a posterior chain movement designed to build strength in the squat AND the deadlift, it starts to make a little more sense.
If you are using a box squat for dynamic work (building explosiveness), then sitting very far back and not having the knees move forward at all is ideal. In this situation, the box height is almost irrelevant. Just go as deep as your can while maintaining a tight arch and the described form above.
If you are using in more of an athletic fashion, or as a basic lift to teach form and depth, then you have to measure your knee and hip crease and at least hit parallel. For me this is about 14 inches. Ideal depth for this is as deep as you can get with strict form.
Another thing to mention is that if you are training for a larger RAW squat with athletic stance/olympic (medium/narrow stance), then the box squat is going to help you much less than bottom paused squats, front squats, and leg press.
This is all my opinion of course.
This might help. Dave Tate explains what height to use.