I can't answer your specific questions but will share my thought processes as I have literally just went through this. I requested supervised visitation as part of my legal separation. Prior to my AH leaving two days ago (per court order), he did keep our kids at times. But it has been in our home. As I thought about how things would be when he is out of our home, in his place or someone else's, I couldn't come to a resolution in my head that the kids would be fully safe, but not just the safe part alone, what would they be exposed to? I realized that if something happened to them, I would never be able to forgive myself. And, flipside, I know he loves our kids and would never intentionally do anything to hurt them, so the decision was very hard for me. But I just can't take any chances, not with my kids.
Oh, and one other thing is that I asked his parents prior to putting in this request if they would supervise. The thought of my kids having to meet their dad in a court ordered situation did not sit well with me. I want them to have some quality time together if at all possible, in a comfortable and familiar setting. I 100% fully trust his parents so I was grateful they were willing to do this.