Whether or not German Cockroaches _can_ fly, as far as I know, under normal circumstances they _don't_ fly. As for Peapers' contention: fleas fly? That's a new on on me (the assertion, not the flea).
German cockroaches do fly. The related species, the Asian cockroach (Blattella asahinai), takes flight more frequently, but both take flight quite commonly.
http://bugguide.net/node/view/33853
Yes. All insects can fly.
----------------------
Update: All insects CAN fly, but not at all stages or states. Ants, for example, do not fly in their normal state, but a queen or a male drone ant will sprout wings and fly during the creation of a new hive.
Yes, they made up numbers in the Luftwaffe.
No, but they are excellent drivers.
dunno but the ones in Texas do
