When I use the default browser (what is it? Is it Chrome? Firefox? other?) to view a site (not necessarily via Google search), does any of that visit information reach Google servers?
How about DNS?
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Actually the predictive search from the address bar sends the text you enter to Google to provide the search predictions. For example, if you start to type "search" and get to "sea" it suggests "sears", "seattle times", "sean parker" etc...
No, the data shouldn't pass through Google servers unless you are viewing a site hosted by Goolge.