My basement is already studded with 1x2. Do I have to replace the studs if replacing panelling with drywall?
No, but you need to be at least 1/2" from concrete and you will be very limited as too insulation you can install. Vapor barrier after on warm side. If you are going to all the expense & labor of doing drywall? why not do it right and put in proper 2x4 studs and insulation, do the joist pockets etc., seal pipes etc. going through rim joist etc. That old 1x2/panel board thing was amateur time back in the day... your basement will actually feel 100% warm then I am sure it did before.
Sorry but there's no such thing as a 1 x 2 stud. This would be called 'strapping'. If you have strapping attached to the concrete wall with nothing to separate it from the concrete that would be a code violation. Also you're required to have electrical receptacles; it would be impossible to run boxes or wires with 1 x 2 strapping not to mention achieving the R20 insulation required by code. FYI, also the old paneling does not meet the flame spread rating required for interior finishes by todays code.
Is it a interior wall or exterior wall?
If it's an interior wall no you don't unless you Planning to put insulation.
If it's an exterior wall then it's probably better if you put the insulation at 20 R and it won't fit a 1 x 2 stud and you've had to replace the 2 x 6 studs if you're planning to replace insulation that is and it would be Recommended To replace the studs in the insulation to keep your studio warm
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