1998 mondeo when brakes applied a beep beep alarm sounds

it could be a seat belt alarm with belts not connected properly
run the fault codes or see a service dealer center for a diagnosis of the fault

May not be the booster as some do make a noise when the brakes are applied. To test press the brakes several times with engine off, Press the pedal down hard and start the engine , the pedal should move down slightly and there should be no whooshing sound . if the above is ok so is the booster.

Diaphragm in the brake booster has busted the sound you are hearing is vacuum from the engine escaping into the cab

your front rotors are warped and need to be replaced

Sounds like you need a brake job performed and the system completely checked over. Check the brake fluid level in the master cylinder, and also make sure your parking brake is not applied by pulling the parking brake release lever.

when you disarm the alarm make sure you hear a beep beep sound twice before you try to start the car.

check your vaccum booster diaphram

What lights are on on the dash, I'd check your fluids (coolant especially) .

in the door is a switch that tells the alarm to activate start there

Have you checked the owners manual for possible causes of the alarm?