It can log that you went somewhere that Google could not otherwise track you. And not just websites; mail, SSH, anything else. I'll wager a fair few people's attempts to avoid tracking for certain activities, clearing cookies, private mode, whatever, has been thwarted because they forgot they'd set this up.
Yes, that is correct. Google use every means possible to track you wherever you go. If that can't get your exact activity, they at least get something.
That's a big distinction though. I don't think Google has the obligation to make sure users are educated and informed. The deceptive practice of Facebook with Onavo is what people object to.
DNS can't log your activity on a website, can it? All DNS does is resolve hosts, right?
DNS service can log that you resolved a host, but doesn't know what you did with the IP address it returned.