First off, let me say thanks in advance for any ones time in helping me.

We are finishing our basement and have the drywall hung. The drywall hangs about 2 inches below the heating ducts. We did not install any boots beforehand for an easy installation of the registers. Oops. There was just a rectangular hole cut in the duct running between the joists from the previous homeowners with the registers being placed directly on the duct. Now that the drywall is up we cannot install a boot. So how to connect the rectangular hole in the duct to the register that will be placed on the drywall where there is about a 2 inch gap?

Also for air return, can I just put a louvre door between the main basement room which is about 1000 sqft and the heater room?

If you enclosed the furnace you will need to supply both high and low combustion air in the amount the unit needs to operate. A louver door migh cut it but that is not the best way to go.

You will have to make a boot connector out of sheetmatal the size of the hole in the main trunk line down to the size of your register opening. Have fun making that one. Short transition fitting OR have a sheetmetal shop make one for you.