Air bubble problem

I am a new pool owner of a 15 year old pool (in ground with 2HP Hayward pump). I will try to summarize a difficult problem (at least for this pool newbie).
I had the pump motor replaced 2 months ago. One month later I had the main bearing seal replaced. I think these problems are caused by my air leak. Here are the symptoms:
1) Water level is constant and the level is good for the skimmer.
2) When I turn the pump off, I can hear air coming in to the basket. (Glugging sound)
3) I can open the basket and it is half full of water. I add water and turn on the pump. After a few minutes, all the air is gone from the basket and the pump works just fine.
4) When the pump is first turned on, there are air bubbles coming out of the jets going into the pool. After a few minutes, there are no more air bubbles as long as the pump continues to run.
5) Vacuum - This does not work or sound good. I turn off the main drain to the pump and I turn off the skimmer. The basket always has air in the basket: air in the top 3 or 4 inches. The pump sounds like it's straining and the Hayward Navigator vacuum barely operates. Before the problems started, the Navigator worked very well.

I cannot run the pump on the timer as I need to prime the basket before running the pump.
Here is what I have done so far:
1) See above - replaced motor and main bearing seal
2) Replaced the seal on the basket
3) Replaced the basket strainer
4) Replaced all the O-rings on the suction side of the pump
5) Cleaned the filter several times - pressure is about 20 psi.

I hope someone recognizes the symptoms. Let me know if there is more info needed or if a picture will help.