I would think they should be on top or release but honestly, why not just create a fixed layout epub?
Targeting only one device makes that easy as iBooks is installed by default already. Interactive PDF is going to require everyone to install a reader and their all nothing but crapshoots.
Levine speaks the truth.
For your issue, I think from a usability standpoint, your users will expect:
1) First Section dropdown contents will open when clicking First Section and will close when they click Page 1/2/3 in section one, and
2) First Section dropdown contents will close when clicking Second Section , and so on.
Nope - needs to be an interactive PDF and that's final. Not my call.
Just to note - they know that everyone will have to have Acrobat Reader installed and that's already in place.