Exploring and optimizing SQL performance of your system (PostgreSQL and Hibernate)?
Get the dynamic SQL generated by Hibernate and ask PostgreSQL to EXPLAIN PLAN.
Log the queries to your database using an aspect.  Add in wall time while you're at it so you can calculate mean wall time and standard deviation.
EXPLAIN PLAN and look for TABLE SCAN
Don't know - it's not under PostgreSQL control.  Better to look into your app server.
Aspects and JMX
Aspects and JMX