Are there any Database functions which allow access to other network services in PostgreSQL
I have never seen that personally, so I looked up all the functions in Postgres found in the docs here.

The only thing it showed remotely close was 'network address functions' in this section.  Outside of that the docs don't show anything for network access functions.  Note this doesn't mean you can't write your own functions that access the system or OS which then can access the network.