Jeff,
Your air pressure will drop to zero for multiple reasons. First, if your coach has automatic hydraulic leveling, the leveling system will dump the air pressure to level the coach as close to the ground as possible. Next, some air leveling systems use the coach air system to level the coach to supplement it's electric compressor. Last, almost all coaches have at least a slight leak in the air system. However, if your air tanks leak down in less than a day without using a leveling system, you should probably check for leaks, because that is a little too fast.
Like David said, your air horn has to have air pressure in your tank to operate, no air pressure, no air horn. Therefore, both of your issues would be considered normal.
Gerald
Gerald