Run procedure at startup

Is there a way to run a pl/pgsql automatically at server startup ?

Is there a way to run a pl/pgsql function with an infinite loop as a daemon ?

Is there a way to start a pl/pgsql function that would persist after the user session has closed ?

Is there a way for an unprivileged user to delegate a task (allowed by superuser) to a superuser ?

Thanks in advance.