Hi,
You can safely remove those navigation links, titles, etc from the layout.master file. For that matter, you can safely remove the menu controls as well and then it won't matter about the site settings or page settings for hiding the menu.
The main required things are divLeft, divCenter, divRight, ScriptManager, ScriptLoader, StylesheetCombiner, MetaData. I think pretty much anything else is optional though I could be forgetting some required ones.
Note that you can also enable per page skins in Site Settings and then you have the freedom to assign different skins to different pages in case you have occasional need for menus on some pages.
Best,
Joe