Water in the fuel, and in the air system would explain both those symptoms.
Let it warm up a bit. Drain any water from the fuel system and maybe change the fuel filter.
See if the engine can build air-pressure when it's a bit warmer and nothing is frozen. It should build and hold 120+ psi, and it shouldn't lose 10 psi when you hit the brakes.
If the system does build pressure, you will hear any major leaks when you shut of the engine. Even small leaks make quite a noise. Leaks that can only be detected with soapy water will not throw those symptoms. They would show as the system leaking down more quickly than it should.