Proxying YouTube with Apache, is it possible?

If you used an Apache proxy, could you (in theory) have your server act as a middleman for YouTube, and use it to filter certain things or allow or deny certain IPs? Would you be able to spoof a legit SSL certificate if you pointed (and the rest of the domains you would need) to the local IP of your server? Also, would you not also be able to cache some videos (I imagine this would take some kind of a special software running to do that, maybe a weird modded Squid or something (idk much about proxies)?

Is that completely stupid and not possible, or is it a thing, or what?