Internet not working on New Release Kali — 2020.1

This should not be the case. If the terminal in virtualbox does not allow you to write + character, install Putty on your Windows box and use SSH to connect to your guest computer. If + does not work in Putty, check the configuration settings, it does work if configured properly.
So you can now use browser and apt-get works with those environment variables set?
If the host computer can not ping 8.8.8.8 neither can your guest do that. The network you have seems to block everything except HTTP via proxy. Here schools do similar things in their Intranet, I guess they must because of wild students but it is a bit annoying.