But the vast majority of the time they are approved, and the nomination begins with politicians. Contrast this to the way the UK does it where the appointments come from the senior judges with politicians then approving or rejecting the proposed new member.
We’ve been launching nuclear reactors into space for decades (mostly RTGs) they’re just much smaller. There isnt any chance of them exploding or anything when exposed to radiation, but yes the chance of the rocket failing, exploding and showering radioactive material over the ocean is why this has to be done incredibly carefully if it is done.