I was thinking that through one Windows Admin Center installation I'll be able to manage several remote Win servers. However, the add server dialog seems to be able to find only local/LAN servers. Is this somehow possible or do I need a separate WAC installation on each server thus each will have its own address?
Of course you can do that! Please check the step-by-step guide below:
https://docs.microsoft.com/en-us/windows-server/manage/windows-admin-center/use/get-started
Make sure you have WinRM & PowerShell remoting enabled, these are disabled by default in Windows 10 and to enable them you type "Enable-PSRemoting" in the PowerShell console with admin privileges. You also need to allow TCP connections from outside of your subnet. Type "Set-NetFirewallRule -Name WINRM-HTTP-In-TCP -RemoteAddress Any" from the same PowerShell console with admin privileges.
Thanks to @joeqwerty assurance I tried more and was successful. The issue was firewall. For somebody, it could be obvious but one needs to allow
Windows Remote Management (HTTP-In)
firewall rule or simply 5985 port. The WAC UI is not very helpful in advising it in my opinion.