When working with catalogs and cross-site publishing SharePoint 2013 automatically rewrites links between catalog items so that those links work wherever the catalog is published.
If you try to hide Navigation Terms pinned from a catalog in the navigation, URL rewriting for catalog items will break and you will see the physical URLs of those items instead.
When switching between the different Device Channels you can persist the choice using the DeviceChannel cookie.
Design Manager allows you to quickly implement your user experience in SharePoint but if you want to build a great public-facing website you should build the Master Page and Page Layouts yourself instead.
When building public-facing websites with SharePoint 2013 you should disallow anonymous users from overriding the Master Page on your website.