If it's the freehub coming loose, not the cassette, that's unusual. I'd check for serious wear inside.
If it's the cassette being loose, that's not uncommon, and I yield to bulldog1935's answer above. Been there.

As far as the braking, any time you mix braking, you can have good or bad results, never seems to be in between:

My key to overcoming this starts at the wheel: true true true.

A trued wheel allows you to move to the next part: clearance clearance clearance. Even if the levers won't pull the distance you need, a trued wheel can let you move those pads right up to the rim, 2-3 mm away, and have adequate braking even with cat/dog matchups on the braking system.

The third part, of course, is the condition of the cabling/housing/clamping.
You are an experienced wrench so this you already know.

Go forth and stop in peace, not pieces.