Why do my brakes apply themselves

Sounds like a dragging brake pad. There is an adhesive that can be applied between the calipers and the pads. Or it may be time for a rear end brake change.

Squealing from brakes when applied (and sometimes even when not) is a common issue with many vehicles. There are a number of reasons for it, most often it is the brake shoes/pads themselves. Most manufacturers today install ceramic brake pads as OEM parts, but due to their cost, most drivers opt for semi-metallic pads when replacing them. Most manufacturers recommend anti-squeal shims and/or compound be applied to brake pads for disc systems, but they are often ignored and not installed. Older, sticky calipers can also cause poor release of brake pads, resulting in drag and noise. Lastly, worn, warped, and thin rotors can add to noise issues. Having well serviced, quality brake parts and using proper installation techniques will usually remedy brake noise issues. Just as a side note, residual dirt and grease from the installation itself can cause noisy brakes for a few days/weeks after first install until it is worn off and the pads break in. If you have issue beyond the first two weeks, and you have had them installed professionally, take it back and have them verify that the pads were installed properly.

The problem is most likely in the vacuum booster. It has a valve inside when slight pressure is applied to the pedal, applies vacuum boost to the master cylinder aiding the operator in braking. If you notice applying the brakes several times with the engine off, the pedal will harden in the same fashion. With a malfunctioning internal valve the booster can apply the vacuum boost when not needed.

Possibly a bad wheel bearing. Brakes would get louder as you apply the brakes.

You would need to apply some adhesive to the back of the brake pads.
This is common practice regarding disc brakes.
Quite a few brands are sold in most autoparts stores, and you should ask the clerk to show you some disc-brake noise reduction adhesives.
Once you get one of these adhesives, jack up the car again, and remove those pads. Follow direction as written on the adhesive's package.

What did you replace the pads with? Sometimes inexpensive aftermarket pads will squeak. I like to use only OEM pads and pad shims and never have a problem.

take the wheel and drum off the back and check that the shoes are not worn out on the edges..what happens is the end wears off first but as pressure is applied the shoe moves to where there is some pad left..severe brake dust can do it too. get the brakes checked as soon as you can.to clean and adjust the rear brakes is not that expensive.

it could be because they are dirty. also the noise could be the back brakes. if its a squeaking noise it could be that they are dirty or that they are cheep brake pads and for the first couple of weeks they squeak. also when you got your breaks changed did the break shop cut the rotors because that cleans them up and makes the rotors like new.

hi im dave
hope i can help
when you had the rear pads applied and the discs turned was there noticeable damage to the disc surface it sounds like your e brake cable is not adjusted properly or perhaps the braided wires inside the insulation are seperating along your brake cable causing the rear brakes to not be adjsting themselves properly. Every time the parking brake is applied the rear brakes are self adjusted if they arent being applied due to slack in or a broken cable you will not adjust your rear brakes. This would accont for the flutter in the brake pedal as hydraulic fluid is still circulating to compress the pads against the rotor but the pads arent reaching the rotor.