If you have air in the pump basket, that means you have an air leak somewhere between the pool and the impeller in the pump ... usually it is above ground, but not always.
I would not think that air would let the DE pass through. Either there is damage to one of the fingers, or your backwash valve could be leaking and letting the DE pass by.
Cloudy water typically points to a lack of proper chlorination. To clear it up you need to follow the SLAM process. [slam:1419i68j][/slam:1419i68j]
So, sounds like you may have 3 independent issues currently. All are important, but until the suction leak is fixed and the filter is working properly, it will be hard to SLAM correctly.