Viewing another session's settings
I don't think it's possible. PostreSQL session variables are meant for 
mostly scripts to run in the same session. If you need persisting variables across user, or a place to store state -- PostgreSQL can do that too, just use a table.

From there you can limit access to the table through Pg access permissions or getter-setter functions.

Here is an example of such a scheme, https://www.depesz.com/2009/08/20/getting-session-variables-without-touching-postgresql-conf/