I have a Linux (console only) VPS. It is possible to install Gunbot on this Linux VPS and to access it on my local computer via the Gunbot GUI by HTTPS?

IIRC, in the past this was not possible. You had to use the GUI on your local machine, transfer the config file to the VPS and execute it on the VPS (gunbot running in the console). But this lead to the problem of having no live information in the Gunbot GUI. Yesterday I saw a tutorial where this _seems_ to be possible - but I am not sure.