Character Animator won't launch.

This does sound like it could be a permissions issue. You said your folders are read/write, but does that include this one? https://blogs.adobe.com/creativecloud/permissions-mac-os-start-adobe-applications/

Also, as a good test to see if this is an issue confined to your local account is to temporarily create a new user account. If CH launches with no issue there then it's an account issue, not an app issue.

Sorry to hear both of those suggestions didn't work. Have you tried the simple uninstall (while making sure to remove the prefs) and reinstall?

Try enabling camera and micorphones in System Preferences > Security and Privacy > Privacy.
Please also see this doc.

Your docs folder might have Read Only permissions.

Have you tried trashing your preferences? 

Windows: C:\Users\[USERNAME]\AppData\Roaming\Adobe\Character Animator\3.0

macOS: ~/Application Data/Adobe/Character Animator/3.0