I usually connect it to any bare metal spot in my case when I'm building or taking things out and I haven't ever had a problem. I wouldn't connect it to the radiator though unless there's some unpainted spot than it can clip to that won't hurt the fins.

It really depends on what kind of fridge you have. Most exposed metal is found behind the fridge or under it. This means unless it's a small fridge you're going to need to build right next to it. Some other items that you can probably connect to is a metal caged fan, a bird cage, your PC Case door if it's made out of metal and etc.

I would conntect it to an exposed screw on the outside of the case or a metal chair leg, anything metal and grounded

Could I not connect to the plugged in  lightning adapter?