When I trying connect to my postgres database, I always receiving connection time out error. For instance I want to connect from pqadmin. Can you please help with it ?
PostgreSQL databases on PythonAnywhere are protected by a firewall, so external computers can't access them directly -- you need to use a thing called an SSH tunnel, which opens a secure SSH connection to PythonAnywhere, then sends the Postgres stuff over it.
This help page on the PythonAnywhere site has the details on how to set that up.