Mac Recovery asks for password

I don't think you need a firmware password. When I've reinstalled the OS, I had to choose an admin user and supply that user's local password.

Exactly what year model iMac?

If it is a 2010 or 2011 bought in 2011, then 10.13 High Sierra is the highest macOS that it can run.

If it is a 2012 or later running Mojave or Catalina, then downgrading High Sierra will erase the iMac and you need your parents password to do that.

Viridianne wrote:

It’s 2011 model. My parents want to use it as a display for their MacBook Air 2017 as the screen is too small for movie and music editing.

OK got it.

Auto update was on and the iMac is now running Yosemite. They also want to do a fresh install to clean up stuff.

OK so then it is a macOS "upgrade" from Yosemite to High Sierra that you are wanting.

If and when you get past the firmware lock and startup from Yosemite, click on macOS High Sierra 10.13 using Safari.

I get a screen like this when I boot with Command R:

You should still be able to get into Recovery Mode.

If you are using a wireless keyboard, try using a USB keyboard to enter the Command + R during startup.

Then once you are in Recovery Mode, follow the directions that dialabrain shared

at > https://osxdaily.com/2015/01/28/forgot-mac-firmware-password-what-now/

A prior user had set a firmware password for enhanced security, osxdaily.com may have salient comments on the subject.

FWIW, you cannot use it as a display for 2020 Macs or later.

That screen is asking for a firmware password.

See if this helps: https://osxdaily.com/2015/01/28/forgot-mac-firmware-password-what-now/