how to upgrade iMac (21.5-inch, Mid 2010

To the first question >>

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. Make sure to use Only Safari to commence the download as Other may not work

Make a Time Machine Backup Before attempting. Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina and Big Sur Only support 64 bit and there is no workaround.

Are there any AntiVirus, Disk Cleaner, Optimizers, Defrag, VPNs etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation.

Tat mac can only upgrade to macOS High Sierra 10.13.6.

Here is how,

For macOS High Sierra,

Open Safari and click on this link, 

How to get old versions of macOS – Apple Support

Go to the Download OS section and click on macOS High Sierra.

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS High Sierra.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.