When tightening& locking the head, a slight nod is normal (~.001 max) ,the feel of the Z feed will never be like a drill press but it still should go up and down with some weight behind it, hard to explain but I also noticed the up/down movement will get smoother with use and lots of lubrication.
Consider installing a DRO ,at least for the Z axis, it is a huge upgrade, I highly recommend it.