You can use a cheap "rod type" air pressure indicator but they are notoriously inaccurate. If you have a good gauge you can measure the tire pressure with that and then check it using the cheap one to sort of calibrate it. Fuel pressure should be around 40 psi and hold for at least 20-30 min after shutting down. The air cleaner thermostate doesn't get jammed it just doesn't close off the heated air door after the engine warms up. But since you also have the problem with a cold engine I wouldn't think that was the issue. Try a new fuel pump relay.