I need to install and use FME server on an Ubuntu cloud machine, on distant, via SSH command terminal. Could you please advise me about that? Thanks.

The easiest way would be to probably use docker - however, if not you can follow these installation instructions:

For a silent installation here: https://docs.safe.com/fme/html/FME_Server_Documentation/AdminGuide/Silent-Install-Linux.htm

For normal express installation here:

https://docs.safe.com/fme/html/FME_Server_Documentation/AdminGuide/ExpressInstallation_Linux.htm

It should no problem to restore the backup, however, I would keep the windows version running in case there are issues.