Nectar, as do all Butterflies. The caterpillars only eat the leaves of pawpaw trees though, which is why they aren't found in areas without pawpaw.
Correction: Not all butterflies eat nectar. Yes, the Zebra swallowtail does eat nectar. However, many types of butterflies eat only tree sap or rotting fruit. Others prefer rotting flesh or dung. While rotting flesh and dung may be repugnant to us, many butterflies will fly right past the butterfly garden to feast on the stuff.
All butterflies breath through the admen. (The last body fragment of the butterfly)
3.5-5 inch wingspan.
3-5 days. If it's colder up to 7 days.