Even as admin, I cannot edit DefaultFonts.plist for Notes.app. What am I doing wrong?
Several of Apple's bundled applications are protected by SIP (System Integrity Protection). As a result, they cannot be modified, even with root privileges. The -lO flag for ls will show you if a file or folder has restricted status:

ls -lO /Applications/Notes.app/Contents/Resources/en.lproj/DefaultFonts.plist
-rw-r--r--  1 root  wheel  restricted,compressed 538 Aug 20  2018 /Applications/Notes.app/Contents/Resources/en.lproj/DefaultFonts.plist


If you want to proceed, you'll have to disable SIP, make the modifications, and then consider re-enabling SIP. (I strongly recommend not leaving it off, as it provides valuable security for your Mac against malware and other issues like inadvertent destruction of system critical files.)

If you don't like Apple's procedure for disabling SIP, You'll find many webpages explaining how to disable SIP. Here's one.


https://support.apple.com/en-us/HT204899


However, it's possible that altering the app directly may compromise its code-signed status. (Again, a security feature designed to stop apps from running if they've been modified.) You may need to look for another way of changing the font in Notes.