Windows, not admin: Proxy working in Firefox but not in cmd, why?

HTTP proxies only work with the HTTP protocol (and, to some extent with TCP connections in general, using CONNECT).

Ping doesn’t use HTTP or even TCP. Instead, it uses ICMP. There’s no proxy for this protocol.

Additionally, you’re using Linux/UNIX-style environment variables to set the proxy. This won’t work with “native” Windows applications at all. They usually rely on Internet Explorer’s proxy settings. (The options dialog is also available via Control Panel -> Internet Options.)

Also, there’s no such thing as a proxy reachable via HTTPS. It’s always plain HTTP. HTTPS connections are tunneled entirely, using CONNECT.