Brake run-out is caused by the disc being out of true either due to warping or (less likely) the disc carrier or hub/flange being bent. You would notice general vibration under braking, even light braking, and a juddering in the pedal. The effect on pads would be to wear both pads, and they would sit further away from the disc than if it were running true. This would cause a long pedal.
It sounds to me like you had a sticking piston. This would also explain the low fluid level warning as once the brake was operating correctly the piston would have moved to the correct position; ie pad just touching disc, thus lowering the fluid level in the master cylinder reservoir.
The "three stages of feel" of your pedal was caused by the working side of the caliper bending the disc until it met the pad on the seized side. You symptoms and result all make sense to me although run-out is not strictly the correct wording. Still if it's sorted...
Consider putting new pads in as the ones you've got will be worn unevenly.