Can flyers carry adjacent grounded b2b figures off without that figure having to breakaway and does a hovering character have to break away from a grounded one?

Hovering characters do have to breakaway. As long as they are not adjacent to an opposing character and hovering, they can carry a friendly.

MoffProulx is correct but I just wanted to point out the definition of "grounded" from the General FAQ:
"Replace the definition for “grounded” in the glossary, page 23, with: “grounded: Characters, objects, or terrain that is not elevated or soaring.”"

Note that grounded characters include hovering characters provided they are not elevated. So you are probably not referring to "grounded" figures but to non-flying figures.