The red warning light turns on when the parking brake is not fully released, there's unequal pressures in the two hydraulic circuits, or the level of brake fluid is low in the reservoir. If the level is low, do not fill it. There is either a leak that must be addressed or the front disc brakes are worn and in need of replacement.
A pulsing brake pedal is typically caused by warped front brake rotors. If the pulsing starts right after brake work is done there may be debris stuck between the rotor and hub.