Limit number of simultaneous queries by user
This is not possible now. You have two classes of configuration options


Connections and Authentication, includes things like max_connections
Session/Client Configuration, includes things like statement_timeout, lock_timeout, idle_in_transaction_session_timeout
Role-based settings includes CONNECTION LIMIT (per user).


That's all that the server provides. In order to track what you're talking about the server would have to check pg_stat_activity. You can however get the information you're looking for manually..

SELECT usename AS username, count(*) AS concurrent_statements
FROM pg_stat_activity
WHERE state = 'active'
GROUP BY usename;


You can run a function periodically that checks the above and calls pg_cancel_backend(pid int), or pg_terminate_backend(pid int). See the docs here for more information I don't particularly think that's a good idea. I would work with the default options before I tried to roll my own system based on this.