I have a 2003 Mazda Protege 2

PARKING/EMERGENCYÂ BRAKE

1. On models with rear disc brakes,  depress brake pedal several times. On models with rear drum brakes,  start engine and depress brake pedal several times. Stop engine.
2. On all models pull parking brake lever with a force of 22 lbs. Stroke should be 5 7 notches. If stroke is as specified,  parking brake is properly adjusted. If stroke is not as specified,  raise and support rear of
vehicle. Release parking brake lever.
3. Turn the adjusting nut at the front of the parking cable,  on the side of the parking brake lever. After adjustment,  turn the ignition switch to ON,  pull the parking brake lever one notch,  and verify that the parking
brake warning light illuminates. Then verify that the rear brakes do not drag.

As far as pedal not feeling assolid, turn allen screw in until pads slightly touch rotor then back off 1/3 of turn or 30 degrees

Try re bleeding again and then drive the car and make several slow stops form 40 mph, the pads may have to seat especially ifyou used ceramic pads. Remember r/rear then l/rear, r/front l/front when bleeding. What order did you bleed the brakes in, there is a specific pattern that you should be using to do this. Usually by starting with the line the farthest from the master cylinder and working to the shortest. You may need to adjust the parking brake from inside the car as well