Oracle VirtualBox installation failed on BigSur M1 Apple laptop

High Sierra comes with a new security feature: Secure Kernel Extension Loading, which blocks kernel extension loading. The implementation appears to be questionable.

To allow the loading of some non-Apple kernel extension you have to either allow execution in Preferences > Security & Privacy > General:

or disable the security feature with a Terminal command (not recommended):

sudo spctl --master-disable

I had these same issues installing VirtualBox 5.2 on an employees Mac running 10.13, via remote desktop. After trying all the things you've mentioned I kept googling, eventually finding this thread saying it's a screensharing issue.

There is a report that you cannot allow kext if you are using Screen Sharing.

I use magic perf to intercept various touchpad actions. [...] If you have this problem try to disable any apps that my capture and forward clicks.

Apple are disabling the "Allow" button if it's pressed by anyone BUT the Mac touchpad, directly.

So, if you're also attempting this via some sort of indirect method, or are using something like Magic Perf or Steermouse, disable those and make sure the click on "Allow" is as direct as possible.

Hope this helps someone out there.