What ia the minimum distance between basin and trap(water level in trap)

If you have a pop up it will be 4-6" or more. With no pop up, less. What is the issue? Even with a cut off tail piece, you can't go under 2-3"

If you're asking about the water level it should be up to the thought of the far bend in the trap. This is the wall all traps wok. Regards. Tom