This is very common, especially in homes with older fixtures. When you flush a toilet, for example, the cold water pressure drops but the hot water pressure doesn't drop by as much so the water gets hotter. Newer fixtures can partially compensate for this drop in pressure and are called, obviously, pressure compensating fixtures. In many parts of the US, pressure compensating fixtures are required by plumbing codes.
The air in the lines puzzles me, though. You shouldn't ever have air in your lines, though the pressure may drop significantly when you have multiple faucets open. Are you sure you don't have a partial break in the line that runs from the water main to your house? That might explain the low pressure and air in your lines.