Still, when I first started the graphical interface (VirtualBox Manager), most of text appeared as funny characters that can’t really be read:
This is a common problem when you’re trying to run a graphical (X11) application on a server without graphics system like Xorg. As you probably guess, the problem is to do with fonts.
Specifically, it’s a problem of your remote Linux server not having any fonts installed, because Xorg (graphics system) was never installed on it (servers usually have server-specific version of distro or at least a package selection that disables desktop related things).
Once we install standard fonts package like this:
… restarting application will result in a normal window with quite readable fonts: