Use DC Motor driver for electromagnet
First answering your questions:

Showing the motor attached to the high side and the solenoid attached to the low side is arbitrary; it could be the other way around.  As drawn, the sense resistor could not be used by the solenoid in this configuration, but could be used by the unidirectional motor.
You can parallel the outputs by tying them together on the input and output side if you need more gate drive than you can get from a single output.  This is probably more important at the fast switching speeds common to motors and power supplies; generally solenoids do not require high frequency PWM.
Current limiting has to happen externally; the current sense resistor terminal is supplied as a convenience.  It must be sensed using external circuitry and you have to control the inputs as required.  The IC itself does not sense current.

Solenoid (or electromagnet) magnetic forces are constant only when three conditions are met:  constant current, constant air gap and no motion.  The forces are related to magnetic flux.  As the gap size gets smaller, the magnetic reluctance decreases, requiring less magnetizing force for the same flux density.  So the force will increase as the gap decreases if current remains constant.  If the solenoid armature is moving, it induces a secondary, opposing field, similar to back emf in a spinning motor.  So an algorithm that controls magnetic force will not be trivial and will require real-time knowledge of the relative position of the magnetic elements.
Good luck!