1) You can not move sites from one server to another. This is disabled as you would loose all website scripts and pages if ispconfig just creates the new site on the new server and deletes the old one and moving website data which might be gogabytes in size is not possible with the currently used syncing mechanisms.
2) Then you did not enable mysql databases for the second server in the server settings.
3) Yes, thats the purpose of ispconfig. Manage multiple servers from one controlpanel.