I have a iMac 2010. What Mac OS can I use

What you are at now, High Sierra. For Mojave you would need a late 2012 iMac or later.

A 2010 iMac cannot upgrade any further than macOS High Sierra 10.13.6.

Sorry hermosa, I didn't mean to be so obtuse. (◔_◔)

Any idea what to do with the apps in the app store that cannot be downloaded due to the macOS being out of date?

Leave them there you cannot use them.

What apps were you wanting.