If post-forwarding is an issue, you can always use a free VPN to reach your self-hosted services. Or if you want to keep them public, you can set up yourself a relay on AWS LightSail for less than 5$/month. Or if you want to save as much as possible you can use TailScale or CloudFlare’s Zero Trust network to self-host for free using their server as a relay.

I think so, but only on some devices. As far as I understand, you can only play in high resolution on devices which support stronger hardware DRM. On those devices recording the screen might be harder/impossible.

I never tested this theory though, so please do not quote me on this.

Amazon Prime, like Netflix, unlike YouTube (for now), uses DRM to protect videos. It would be very difficult to download them, and yt-dlp definitely doesn’t even try to bypass DRM.