Could someone tell me whether my OS is communicating with the internet?

I think you're worried about the 8 packets transmitted message.

The ping application generates packets and submits them to the kernel for processing. Those are the "transmitted" packets reported in ping statistics. When packets enter the iptables' chains they can be accepted, dropped or rejected.

Ping says sendmsg: Operation not permitted because packets sent by the application were not accepted. So the answer is no, packets sent by ping didn't leave your computer.

But, as said by Alaa, you pinged www.yahoo.com and the name was successfully resolved to an address (206.190.36.45). This only happens if your computer sends a DNS query and receives a reply or if the name is in the DNS cache, which shouldn't happen by default (thanks @Alaa).

Are you sure all the traffic is blocked if VPN is disconnected? Maybe you didn't block DNS. You should only accept output traffic destined to your VPN gateway.