Child theme is essentially a different theme than its parent theme, so when you activate a child theme, WordPress considers it as a different theme and so reverts your background and header back to the default settings.
I see now that the secondary menu has actually lost its styling altogether (i.e. it displays as a vertical list with bullets). Let me know if you still need help with it.
This free Support Forum relies on contributions from our support staffs and fellow Graphene themes users. While we endeavour to provide adequate and timely support, due to its voluntary nature responses are not guaranteed and may be delayed.
If you require urgent assistance, you may like to consider our Priority Support option.