I understand how the logic levels of an NMOS work with a pull-up resistor. 1. What would happen though if there was no resistor attached? (What would the logic levels look like and why?) 2. What would happen if there was a pull down resistor instead?
N channel mosfets when used in a typical switching configuration connect their output to ground when turned on and leave their output disconnected when turned off.
So with a pull down the output will be permanently stuck low. With no pull at all the output will switch between ground and floating. In the absense of any external influences a floating output will generally stay where it was last set so again the output will be stuck at ground.
Note that there is a trick involving a N channel mosfet with special geometry that can be (and usually was) used as a pullup instead of a resistor.