There should be a return spring on the brake pedal, so it should spring back anyway. I think the brake lights are operated by a microswitch on the brake pedal, so if the spring has broken to pull the pedal back up, this might account for the pedal not returning and the brake lights being on. The handbrake shoes might be sticking on but that wouldn't affect the hydraulic brakes. I suggest going around each corner of the car to make sure the pads aren't binding in the yoke that holds them, and the calipers aren't sticking on the slider pins. Sticking pads usually shows up if the pad on one side of the disc is worn a lot more that the pad on the other side. Sticking caliper shows similar but the lining on the pads may also look to be tapered.
I routinely take the caliper off, pull the pads out, and the thin shims in the brake yoke. Clean up the shims, and the grooves in the yoke where they sit to remove excess rust and scale. I also lightly file the ears on the pad backing plate to remove rust and sharp edges that can dig into the shim and make the pads bind. Replace the shims, then refit the pads with a smear of brake grease to lubricate the ears where they slide along in the shim. Pull the slider pins out and check they aren't corroded. Lubricate them with brake grease and slide them back in, making sure the sealing boot is fitted and not split. Make sure the pins slide in and out freely. Brake grease has to be the type compatible with rubber parts, I bought a pot of Permatex 24110.
Before refitting the caliper making sure the piston hasn't seized by pushing it in a little. At least then you can be sure it's not the pads or calipers causing the issue. There are no springs as such in the actual brakes to make the pedal spring back.
