Can I use 120 film in 220 SQ backs? I know this works fine with Mamiya backs.
What exactly do I need to build an SQ system (body, back, insert?, finder etc).
You probably can; there are two problems. The first is unlike 220, 120 has paper backing over its entire length which means it's going to be thicker. That could lead to a bit of stress winding the film thru, or mess up the spacing between frames a bit.
The second is that 220 will assume 24 exposures so you'll have to keep an eye on the frame count and then do a trick to wind the film thru without taking frames 13, 14 and 15 thru 24 on the paper trailer.
You need a body (ideally with crank and focus screen), a back with insert, a viewfinder and most essentially, a lens (unless you want to do pinhole

).
I quite enjoy mine -- I originally planned to go minimalist -- one body, one back, a WLF and an 80mm lens, but alas, I've had
a few GAS attacks since. 