Can the farm administrator log into any SharePoint site on that farm?
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By default member of farm administrator group don't have access to the site content.
In order to give them rights on site collection, either you need to add them in policy of webapplication (this will give access to all sites col in that Web app) or add them individually in each site collection.
Read this for more info: https://technet.microsoft.com/en-us/library/cc263291.aspx
Not in SharePoint 2013. User needs to be given access to particular sites at some level (Site Collection Admin or adding to Owners, Members, Visitors group)
Let me know if you have any questions