09. How can I check in which of these modes an installed database is running?

There's no API that exposes this. But because you're on a server, you can check what process is running.

I.e. on Windows (Task Manager) and Firebird 2.5:

• One fb_inet_server.exe = very likely SuperClassic
• Multiple fb_inet_server.exe = very likely Classic
• fbserver.exe = very likely SuperServer