Short answer: The proxy will see your IP but does not share that information with us. To prevent the proxy from reading your content, we need to end-to-end the communication (and prevent statistical attacks based on the size of the encrypted data and so on).
Regarding Tor: Yes, we experimented with sending through Tor. The main issue is that our code needs to run in a WebExtension, which is a restricted environment. You can only use WebSocket communication but no real TCP sockets. The next blog post in the series has more information and has a link to the code of our experimental Tor client (the native Tor client compiled with WebAssembly to be used in a WebExtension).
I hope the post will address your open questions. If not, you can ask tomorrow about the details of HPN.