My question is: can we use Nessus to perform a scan on a remote server? Or is it used only to perform scans on the local network?
I am not sure what you mean "on a remote server" but very simply put: yes, you can - as long as you're authorized.
If your scenario is to scan server which lies outside of your local network (for example a different server belonging to your company, hosted somewhere else) Nessus is your choice.
If you mean you want to perform a scan from a remote server with Nessus, that's possible as well. Our company uses Nessus on a dedicated server for external scans.
But be warned - don't scan server which you're not authorized to.
I also believe trial version is only for non-commercial scans.