Composite is monochrome output on the Amigas, not sure why. You need to connect it to the RF out/TV out.
No, the 1200 has colour output on composite. It's probably a PAL 1200 on a NTSC monitor, some monitors will "roll" others will have no colour others won't show anything at all if you have a PAL/NTSC mismatch. You could try holding down both mouse buttons when you turn it on and go into the boot menu and select "NTSC" and boot. Not 100% sure that will fix your problem, but it's worth a shot.
Len