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Does the noise happen all the time you push on the gas pedal or only at certain speeds?
A vibrating brake pedal is an indication of a warped rotor. Noise is common to disk brakes but depending on the noise it can mean that the brake pads are worn out and you are due for a brake job.
If the pedal is stuck down, no vacuum to the release diaphragm on the pedal
Your brake booster is malfunctioning
an air leak in your intake will cause the engine to rattle. Protege's intake hoses are prone to cracking.
You could be very low on oil, check your oil and add to the full line.
That could be any variety of things, of a combination of them, it would be best if you take your car to a trusted mechanic.
What would cause a grinding noise after a tire is replaced and the brakes are not worn?
It would help to specify the type of noise and type of vehicle in question.
Vacuum brake booster is defective or the hose going to the booster is leaking.
If you are not losing brake fluid I would say the master cylinder is bad. Can you tell what direction the occasional noise is coming from?
Letting go of the pedal or pushing the gas pedal.