volume control
there is no option in system preferences>keyboard to use f10 f11 f12 keys for volume.
iMac 27″, macOS 10.15
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in System Preferences > Keyboard, see wether "Use F1, F2, etc. keys as standard function keys" is checked.
when it's selected, you need to press the "fn" key for F10 thru F12 to act as volume control. when it is not selected, F10 thru F12 act as volume control without pressing the "fn" key.
if that's the option that's "not there" you can try and set up a new user, and test. then we know if the issue is system wide or isolated to your existing account.
please see Set up users, guests, and groups on Mac