Is it possible for the Commander of the division to be a higher rank than Major General (mainly Army)?

It's possible, but not probable. Division Commanders are usually newly minted 2-Stars. They have done their time as Deputy Commanding Generals for Divisions and then have moved on to a staff job somewhere to wait for their 2nd star. They serve some time in a staff job as a 2 star and then move into division command. If they are going to be selected for 3 star, they are moved out into a position that will be conducive to their next job. The process at that level is very selective and thoughtful. The powers that be aren't going to let a GO sit in division command as a 3 star general.

Almost anything is possible. But i looked up a list of past commanders of the 82nd Airborne Division and though there were 4 Brigadier Generals on the list there were no Lt Generals....

I'm not 100% sure but from experience I only seen 2Stars serve as Div generals, three stars is someone in position of for example Chief of Army Reserves or National Guard.