Congrats, welcome to the cool club! Here’s some possible help:
Did you verify the z-axis homing switch is normally open and closes? If so, is the spindle mount fully pressing the switch enough to close the contact?
2 and 3) It takes a little adjustment of the belts, V-wheels, and stepper motor potentiometers to get it dialed in and get smooth operation. When something is preventing smooth movement (such as tight V-wheels), it leads to what we’ve called “lost steps”. Here’s two good forum threads you can use to help get the V-wheels, belt, and potentiometers dialed in. The second has a video I made that shows how to adjust the potentiometers to boost power to the steppers: