Condensation is definitely a concern in colder weather. If you create a thermal break that isn't properly sealed against air leakage, warm air from the house will seep behind the walls, bringing lots and lots of moisture with it. Meanwhile the bricks, which are now insulated, are going to be very very cold, and when warm air gets cold it lets go of its moisture - and thus we get condensation.
That condensation would then get trapped inside the walls - and long before you have a problem with brick deterioration you're going to have mold issues that lead to health issues.
The best thing to do to prevent this is to insulate with a substance that also serves as a vapor barrier, which will prevent any air (and thus any moisture) from leaking into the closed cavity. The best product for this IMO is spray foam insulation, because it fills in all the nooks and crannies and IS the vapor barrier.
Alternatively, you could use fiberglass and cover it over with plastic to form a vapor barrier, and this can work IF you properly seal it all the way around the edges, seams and any holes that occur.
Either approach, however, is going to require you to sacrifice living space, as for a proper thermal break you're going to probably want at least 4" of insulation.
Now - with regard to insulating your spare rooms. Don't insulate your interior walls. Put proper insulation in the external walls of those rooms, so that they don't lose heat to the outside. Yes you will be heating them, but if they're properly insulated they're not going to cost much to heat and there are numerous other concerns with turning an inside room into a "cold" room - it's a finished space, after all, and you don't want to risk damaging that by letting it be freezing cold in there.
Yes you can set drywall directly to the block wall. If it intersects with an exterior wall that is exposed to the weather, I would place a layer of poly of out of the intersecting corner, if accessible, out no more than 2', 18" would probably be better, vertically to prevent any moisture coming through the block and getting into the sheetrock. Use drywall clips to hold the corner, so no nails go through the plastic. If it does not, ignore this recommendation.
To mount the drywall use a glue in the large tubes, you will go through a lot. Blob on golf ball sized portions of glue on an approx. 16"X16" grid. Set your drywall onto that and secure directly into the block with drywall nails. that is if they pass the test.
To test your nails drive a few drywall nails into the face of the block before you start your drywall install. Do not nail in the joints, the mortar is much denser. On true cinder block, not slag block, (slag block is a newer process ) I have run 1 1/4" drywall screws right into the block, that may do what you need right away. Other nails to try just to hold the sheetrock long enough for the glue to grip are roofing nails. Find one of theses that is suitable for your install.
After you sort out which fasteners to use, hold the sheetrock tight to the wall in the place you want to nail or screw. Set your fastener, some help here would be beneficial and set a few more before you move down the sheet to add more. The amount of fasteners needed will be only enough to hold the sheet flat, the glue will do the rest.
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A vent isn't hard to extend. Any decent contractor could extend your current vent to closet wall. I am assuming this is the outside of the closet too - you don't ever put a vent in the inside of a closet and not even sure that is code. Anyway you need to part ways with this contractor if you can. If he even thinks about telling you something that dumb then who knows what he is doing when you aren't watching.