My logs are constantly filling up with these messages for hundreds of tables:
WARNING: skipping "some_table_name" --- only table or database owner can analyze it
How do I perform any the following and/or resolve this?
Side note: none of the log file rotation, truncation, size/date limits settings are working either but I'll save that for a separate post.
It sounds like you revoked superuser privileges from the cluster's founding user. Don't do that. Log in as your remaining superuser, and grant superuser privileges back to the founding user. If you have no remaining superusers, then you need to shut down the server, start it up in single-user mode, and regrant superuser privs.
The founding user is the username specified to initdb's -U argument when the database was created, or if that argument was not provided, then it is the name of the OS user who ran the initdb. This is most often
You need to restore postgres' rights to superuser:
ALTER USER postgres WITH SUPERUSER;