I had this exact situation when flashing around a chimney leaked and I had some water spots on the ceiling by the fireplace. The stains from the water can still come through even after the drywall is dry, so you need to apply a sealer and repaint. I used Kilz; you should be able to find a similar product if that's not available where you live.
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.
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I would lean heavily in the direction of stripping to the studs and then attaching the MDF to the studs, but that's making the assumption that the MDF is of some reasonable thickness (12mm / 1/2 inch or more.)
Fix anything that needs fixing in the wall cavities while you are at it (insulation, wiring, plumbing, etc.)
Sheeting over poor-quality plaster/drywall reveals in great detail exactly how non-flat the substrate is, and eats space in the room. Despite the brief mess, starting fresh may be faster overall (as you are not compensating for all those humps and hollows), and result in a better job.