XMLSitemap- Is it OK to add nodes both by content type and menu?
There is no harm in adding both by menu and by content type (I have tested this before).  In my experience, paths will not be duplicated.

If you also add by content type, then that priority will be used, even if it is lower than the one you have set for the menu.  Also, the last modification date will be used; it doesn't get used when you add by menu.  The XML Sitemap module also checks node access rights, so only ones visible by anonymous will end up in the sitemap.

If you add by menu, the module will not output links that the anonymous user doesn't have access to.

I don't recall explicitly testing paths that exist in multiple menus, though.