Is there any info as to how large/small this server is?
https://developers.google.com/speed/public-dns/faq
"Where are your servers currently located?"
"Google Public DNS servers are available worldwide. There are two answers to this question, one for clients and another for the DNS servers from which Google Public DNS gets the answers it returns to clients.
When clients send queries to Google Public DNS, they are routed to the nearest location advertising the anycast address used (8.8.8.8, 8.8.4.4, or one of the IPv6 addresses in 2001:4860:4860::). The specific locations advertising these anycast addresses change due to network conditions and traffic load, and include nearly all of the Core data centers and Edge Points of Presence (PoPs) in the Google Edge Network."
If I decide to use Google DNS, I always choose 8.8.4.4 first with the superstitious hope that it will respond faster than 8.8.8.8.
In terms of number of servers, I don't think that's necessarily knowable without inside information (although maybe there's some metadata available). Obviously, incoming requests are load balanced or load balanceable at the PoPs where it's provisioned, so we can't count that. Outgoing requests could easily go through a gateway (or gateways) as well, so we can't use number of IPs as any indication either.
I don't think there are public usage stats either.
So, lower bound, one server per PoP (but, they don't necessarily need all PoPs online) and no upper bound.