Sinking brake pedal

Welcome to 2CarPros. When you say sinking do you mean you can step on the pedal and it slowly goes to the floor or that it seems to get lower every time you apply the brakes? For the first one I would look at the master cylinder you replaced. Have seen many that would leak past the internal pistons that were new out of the box! Was the pedal sinking prior to the replacement? Did it start after you bled the brakes? If yes a common reason is that crud builds up in the piston bores where the two pistons normally don't reach under braking, when you bleed them it is easy to push the pedal too far and the seals run over that area and it acts like sandpaper on the rubber and you get a leak. On "new" ones I have seen where they machine the bore too large or on rebuilt ones they honed the bore out and the replacement seals are not a good fit.
If the rear shoes are the wrong size for the drums they will not seat in properly and you get the chatter you talk about. You can try using the adjusters to see if it will help. Tighten them until you cannot rotate the drum at all, now back them off until you can just rotate the drum. Step on the pedal a few times and be sure the parking brake is fully off. Then adjust them again. Back the adjuster off until the brakes just release and have a slight drag. Then drive it around the block a couple times while gently applying and releasing the brakes. Now pull the drum off and see where the shoes are making contact. Ideally you want contact across the entire surface of both shoes.