There seem to be 2 ways of seeing both the list of participants (if you are the host) and "Chat": the one version does flash up in the middle of the screen, which could be distracting to anyone performing at the time, but for the other, it all appears in a column at the right-hand side of the screen, away from all the mini-screens of the various participants. How it appears has something to do with how you set screen size, and the latter version is what I find easier to work with.
As for appointing co-hosts: I have tried to do this in advance of opening a meeting, but my requests were turned down as the people I nominated were not deemed to be Zoom account-holders (does these mean you have to be a paying Zoom member, as opposed to one using free Zoom? Seems so). However, with one session I host, I do largely hand it over to a friend to MC once we are all in, in terms of deciding who goes next. I just sit wielding the POWER over anyone who fails to mute voluntarily, and also put up any music scores required via screen sharing, and scroll them down/up as required.