You must create a disk database on your external hard drive. You’ll reconnect to this if you move to a different computer.
As of Resolve 16, you can now change the resolution of individual timelines within a project, but you can define the default resolution in Project Settings (Shift+9). Deliverables can still render at “source resolution.” Scaling is a project preference. Timelines and media are separate in Resolve; a much more scalable approach.
Setting Media Locations
Playback preferences for underpowered systems.
It’s still possible to cmd+e export a project file from Resolve. Or right-click in the project window you see when Resolve opens and export the project from there.