howto configure heath monitors for proxy server checking for google.com website

You could probably very simply create an FQDN-based or static IP-based pool of Google addresses and apply a monitor of some type to that pool (icmp or http get), and then query for the status of that pool in an iRule. But why do you want to do this?

To monitor the proxy in the pool and are able to go the internet. We had some issue with licensing where the proxy server was with port 8080, serving the request as asking for passwod, but users unable to the internet.