What you’re talking about is a proxy server, I have done proxies and reverse proxies and don’t have a configuration I’ve encountered that I could recommend.
This is a cat and mouse game, streaming services are pressured by rights holders to respect their contracts, VPN providers (thus far) are not liable for users violating their agreements by using a VPN to bypass content restrictions. This will likely be a case of sometimes it works sometimes it’s blocked.
This is too vague. How are we defining performance? If you have gigabit internet but a 10 Meg VPN service you’ll be limited by the smallest connection in the chain (there is no “performance loss” just a lot of untapped potential). Also, if your proxy is underpowered for your configuration, that would impact performance of the firewall/proxy combo device. On top of those, when you add the proxy connection and the connection through the VPN you will have higher latency as compared to going directly to the internet out of your ISP, is that “performance loss” or not? After all, the connection would still be operating at the speed of light, it would just be going further than it was previously to get to the same place. Latency will degrade the end user experience, but that doesn’t necessarily mean any of the technology is working sub-optimally.