Firefox’s free VPN will offer 50 gigabytes of monthly data, which is pretty generous for a browser-based VPN. A Mozilla account is required to make use of it, which isn’t a hardship (they’re free), but is a point of friction some may wish to know upfront.
No, not at all. You have 2 encrypted connections A to B and B to C, where B is the proxy server. The proxy server decrypts AB, sees the plaintext traffic to check against rules, then reencrypts the traffic with his own key and forwards it to B to C. Your browser on C sees the proxy servers cert for BC, and the website and proxy handle out a different cert AB. No encryption or cert is broken during the process.