Good news! Your Whonix system is mostly working.
This is normal. Whonix-Gateway eats pings. https://www.whonix.org/wiki/FAQ#Why_can.27t_I_ping_the_Whonix-Gateway.3F
This is not normal. But judging by the following result, you are able to connect to sites on the net. So this may be a Tor Browser issue, similar to: https://forums.whonix.org/t/anon-whonix-qube-proxy-error-tor-disabled/3299
Let's do this first. Normally, you could just do
sudo apt-get update && sudo apt-get dist-upgrade in your Whonix templates. Unfortunately, we had a rather eventful week: https://forums.whonix.org/t/apt-get-upgrading-security-issue-cve-2016-1252/3288. And the best recommendation in terms of security is for you to re-install your Whonix templates: https://www.whonix.org/blog/whonix-13-0-0-1-4. [You are obviously free to make your own choices - the old templates can still function correctly. Personally, I would re-download and go make a cup of coffee and enjoy some peace of mind. ]
Once you've got your templates installed, run
sudo apt-get update && sudo apt-get dist-upgrade in both of your whonix templates.
Let us know if it's still not working and we can take a look at some firewall rules.