Don't forget Google's free hosting of Javascript libraries and webfonts. The cost of serving those is recouped by dropping a cookie on you. Also Google DNS can give them great insight into domain popularity.
Only if you allow third-party cookies. I'm honestly amazed that browsers haven't moved to turn third-party cookies off by default.
Google's entire business is based on building large database of tracking (and other) information; obviously their DNS is just another data source.
Just skip the recursive resolvers and run a local caching DNS server that starts from the root zones.
And the IP may be a public network.