the battery specs would be available by application, so if it calls for a specific group, then that is what you should get. the store where the batteries are available *should* have some sort of chart to be able to verify the battery needed.
as for the starter, the solenoid doesn't spin. the armature inside the starter housing does. the solenoid simply engages the lever to push out the bendix, which will engage the teeth of the flywheel or flexplate.
a click *bzzzzzzzzzzzzzz* sound is usually an indicator of a worn bendix that is freewheeling. they are supposed to lock in the one position to apply torque to the flywheel, and spin freely the opposite way to be able to disengage when the engine is started.
bendixes are not (usually) available for the bmw's. at least i have not ever seen one listed as an available part.
besides, for the amount of labor involved in a 1/2 reman attempt outweighs any cost savings from sourcing a quality reman unit. i'd look at going that route.