Q1: For Z you need a ballscrew bearing block with a pair of angular contact bearings to take the axial thrust and support the weight of the spindle. The bearings in the motor are not designed for that amount of load. This is usually at the top of the ballscrew.
At the lower end of the ballscrew it is better to fit a bearing but I think you can run without one.

Q2: I would not use 2 bearings on the Z axis, it needs 4. Also I would swap them around so the bearing blocks are on the Y axis and the rails are on the Z axis. Then add a Z axis plate to mount the rails to on one side and the spindle bracket on the other.

Q3: 15mm side plates are OK, 20mm is preferable.

Q4: For what you have drawn a pair of Nema 23s with the right power supply (~70V) will move that no problem.

Q5: Can't quite see the detail around the interface of the gantry side plates, but make sure there is a good connection down to the bearing blocks.
Do you already have the 15mm rails for X and Y? If not, go to 20mm.