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.

You should.

Something is needed to seal the new drywall. Primer is much cheaper than paint. The basic rule is if you want a wall to look uniform, you have to prime it first.

If this is a paint + texture can, when left unprimed, the drywall will suck all the paint from the texture into the wall, leaving an uneven mess behind. If you're going to paint after applying the texture, I'd prime in between as well; the natural unevenness from the spray will lead to splotchiness.