Why is a feather check performed on a piston engine and how much RPM drop should be allowed?
The check is performed to make sure the prop will actually feather when pulled past the feather gates.  You'll be in a world of hurt if you are not able to feather a prop if the engine quits.

A couple hundeed RPM drop is acceptable (generally).  So called "deep cycling" props does nothing for you.  I suppose that there are some goofy mechanisms on oddball planes that require a deep cycle but the vast majority only require you to observe a small drop.

Remember, you are checking that the governor can control the prop, not how far the prop can travel.

Edit 1: I should add that you should just do whatever the POH/AFM tells you to do.

Edit 2: a pilot is typically looking for an oil pressure change, manifold pressure rise, and an RPM drop with each prop cycle.