Ouch...there is a small Allen head bolt on the left side top of the rad to let trapped air out...when coolant comes out, close it.
To check fan, touch the two wires together at thermostatic switch at top of head when running. You may get shocked.
I have had trouble finding a replacement cylinder for my techno so replating is probably the best route for you. Beta's use vertex pistons. I paid aprox 200 for mine years ago.
My cylinder finally corroded away at the o ring seal and now exhaust goes into the coolant so I'm out of luck.
Good luck with yours...mine was a great bike for years.