No, you must use the IC box SKU# 118-376 to use this recess unit in an insulated ceiling

IN SHORT; YES THESE UNITS ARE IDEAL TO BE USED IN A DROP CEILING APPLICATION, BUT PLEASE NOTE THAT IT IS HIGHLY SUGGESTED TO USE A CERTIFIED ELECTRICAL CONTRACTOR FOR INSTALLATION OF RECESSED FIXTURES.
PLEASE NOTE THAT THERE ARE MANY BUILDING AND ELECTRICAL CODES THAT MUST BE FOLLOWED WHEN INSTALLING A RECESS UNIT IN ANY RESIDENTIAL/COMMERCIAL APPLICATION

The connection box attached to the recess unit is only approved as a connection box, not a junction box

The simple answer is no.
An "R" lamp should only be used in a fixture that is specified to accept "R" lamping. The unit in question can only be used with the designated lamping, in this case a "PAR

In short-Yes.
Please use VHG-4I01 to make a TH-P11B-22 insulated.

There is no universal cutout diameter for a 4" pot light since all the manufactures use different diameter cans, so its always best to refer to the installation instructions included with your purchase.
But, for the Next Lite 4" units, a 4 1/8" hole is required for installation.

Part #VHG-4I01 is and insulated box the MUST be used with the unit above in and Insulated application.

You will need to make a 4" hole and maybe you might have to sand the sides to another 2mm or something so that the pot light would go in smoothly.