Ping times will be high for some sites, but I doubt Google will be one of those. As soon as this Lunar Net goes up Google will have a server on the moon faster than you can say 'light-speed delay', so all your favourite Google services and YouTube videos will be available locally with nice low ping times. It's the rest of the internet you'll have to wait for.
Yes, Google will have servers on the moon, but I doubt they'd have a mirror of all youtube.
Latency wouldn't necessarily affect watching a youtube video -- sure it would start slower, but latency != bandwidth. If you set your TCP window size high enough and could ensure low packet loss you could get some pretty fast transfers going.
I suppose that also assumes gigabit+ radio links to span the distance.
Agreed, but to mirror all of youtube is redundant, the vast majority of people only watch the most popular videos. By providing a selection of 'this weeks best' you will surely provide low latency for the majority of files. Similarly ISP's can start doing site caching for popular pages providing lower latencies for popular sites and pages.