You're referring to the brake booster the round black box.
When you pump the brake pedal you're suppose to hear the sound of the air compressing, that is normal.
Brake leathers? Broken brake booster? Have you checked the brake lines for leakage? What about the brake master cylinder and the brake fluid reservoir?
What kind of a mechanic is he? Repair a brake booster? Who on earth does that? You replace it not repair it.