You don't mention the pump model in your post. If you fill your
signature with pool info & model numbers and other info per the
suggestions. It can help us easily identify what equipment you have installed.
Back to your question. There is a mechanical seal between the pump housing and the motor. If the seal was bad you would get water leaking out, not air in the pump. The Hayward pumps do have a fan in the back near the speed/off switch that will blow air to cool the motor. This is normal, it is direct drive off the motor shaft and air flow will change based on speed. You probably just never noticed it.
Air in the basket usually works its way out under normal conditions. Air in the basket almost always means air is getting in from somewhere, aka a leak. It could be your basket cover gasket, pinhole in your suction line, poor connection between hose & fittings, too low of water in your pool, etc. I would go out with a screwdriver and make sure the clamps are tight (remember too tight is broke, lol). Take the basket cover off & grease (with silicone) the o-ring. Look for cracks in the basket housing/cover. Unplug the pump!! and see if you can feel around the impeller inlet to see if there is gunk in there and if it spins freely. Check to make sure all your valves are all the way open before you restart.
I have a 2HP Hayward pump and found that I have to keep the pool water level higher than "normal" because the pump will suck too much water from the skimmer and pull air into the suction line. Most AGP pumps sit below water level and therefore there is actually pressure at the basket inlet and not a vacuum. This is from the head rise up to the pool water level and the relatively short suction hose length.
If you can, post a picture of your setup and maybe we can help you diagnose it more if those above suggestions don't work out. Keep us posted on your findings.
- Dave -