Your problems are the same thing.
If the first layer height is too high, then the raft is NOT properly bonded and just lays on the surface of the bed however it falls from the nozzle.
NO, your Z screw is not loose, clearly you were never told how this all works.
When you turn on the bot, it has NO IDEA in the world where the axis currently is. There are no position sensors on the motors, they simply blindly move forwrd or backward the number of steps they are told. So, we home (move the axis towards a limit switch in a KNOWN location) and then in the memory of the controller set that position to be a corrected value. For example, when you home to Y max, the gantry moves back until the magnet in the carriage triggers the little black hall effect switch in the left rear motor bracket.
In the same fashion, Z homes by moving the entire extruder carriage to a fixed coordinate over the bed and raises the bed until the magnet underneath triggers that limit switch in the front bearing aluminum bar of the extruder carriage.
The giant problem here is several fold. Magnetic proximity switches can be unreliable in an exacting distance sitation where we need it to repeatably trigger at less than 0.1mm variance. Problem 2 is that the bed system glass could be not properly seated on the aluminum build platform and causing the variation. If you magnet fell off and is just sitting in the little pocket on the aluminum plate under the glass, that too could cause variations of when the switch is triggered.
The KEY concept is that the switch and when it is triggered as the bed rises is the cause of your problems, not the Z motor or the screw.