Is there a list of the types of Player that LibreTime supports?
any client that supports the icecast protocol can tune in to the included icecast server, this includes players like vlc ad others. The is a list of " Mediaplayers that support Icecast streams" on 3rd Party Applications — Icecast
To how many player servers can a single live stream be sent?
the amount of concurrent listeners your icecast instance will support is dependant on the bandwidth available to the installation.
I did some off the cuff calculations about supporting 2000+ listeners that may be found in a GitHub comment here a while ago. you should be able to use the same kind of calculation to figure out what is possible in your case.
For example, 2 servers, or 2 installations, one for the playlist/dashboard and one for the players.
my community radio setup is unusual as it has the individual components of libretime on a virtual machine each. We have a icecast server at our site but most listeners will connect to a simple icecast relay server that runs on a VPS with ample bandwidth.
A more typical use-case for LibreTime is a full install on a dedicated VM with enough bandwidth for the amount of listeners you want to serve. This could be on a high-speed fiber internet connection or even a cloudy VPS.