No, it means no 3.5mm headphones without a lightning to 3.5mm adapter that Apple will gladly sell you for $29.
Anything is possible. Chances are though, to parrot others on this site, the removal of the headphone jack is to make it thinner or to allow for more internal space.
I haven't seen any rumors that include wireless charging. everything I've seen seems to suggest that the lightning port will also be used for the charging and headphone. I'd post sources, but can remember where I was reading that (other then on here)