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I have a 2K monitor (2560x1440) on my Win 10 Host.
I would like to run my Win 7 guest machine at full screen but with Full HD resolution (1980x1080).

Is there a way to do that?

At the moment I'm not able to do that for 2 reasons:
1) 1920x1080 resolution is not available in the guest OS (how to add?).
2) If I change to a lower resolution the guest OS, the client area becomes smaller than the available screen area.

Any help appreciated.
Thank you.

Practically speaking, no, there's no way to do that, and you wouldn't want to do it anyway. Scaling 1920 up to 2560 is a non-integer scale factor, so it would look horrible.

Re how to select 1920x1080, if the Guest Additions are installed then that dimension will probably be available on the View|Virtual Screen 1|Resize to xxx by yyy list. Otherwise you can simple drag the virtual monitor to a widescreen aspect ratio and restart, after which Windows will know that it's a widescreen monitor and so should start offering other widescreen settings.

I find that older guests look their best on a 4K monitor if you (a) select a display setting in the guest that can be doubled in size while still fitting on the host screen, and then (2) when the VM is running select View|Virtual Screen 1|Scale to 200%. IME no other scale factor looks good. Do NOT select a global display scale factor in VirtualBox Preferences. Scaling and full screen don't work well together.