Hello Ernest,

redirect back to the mobile is normal, because after some seconds of inactivity the mobile user is forwarded back to the mobile site. This can be changed under 'Plugins settings' -> 'Inactivity time interval to revert to mobile template'

About the menu, it could be a problem of module assignment, when you switch to desktop from mobile. Eventually check if the menu has assignment to certain page only instead of to all pages and change it.

Best

John