Well, to answer your first question: As Mongo stated, Yes there are exchange programs between the AF and Navy. Not many, but the few slots available have been ongoing on and off for decades. I believe there is a Navy exchange officer flying F-22s now at Langley, or there was one there until recently (particularly important to the Navy as they prepare to receive their first stealth platform, the F-35).
Other interesting fact, the AF and Navy do quite a few exchanges with some of our closer Allies, especially the Brits AND the Aussies. Had Brits flying in our Eagle squadrons all the time. Aussies as well. We fly the Brit's Harriers and Tornados, and the Aussie's F-18s (and until they retired the last ones this year, their F-111s as well).
As to AF pilots qualified on Navy fighters and visa versa? Well, the test aviators from both services become qualified in A TON of different platforms, including every fighter in the US inventory. So YES, you can get a chance to fly Navy F-18s (actually, they are owned by Edwards) if you want to fly for the AF, and Navy guys fo get a cance to fly our stuff. The Test School pool of qualified aviators is VERY small, and the competition to get into TPS is extremely difficult (and don't ecen try if you don't have a technical degree, preferably at least a Master's).
As to who ferries jets to our Foreign Military Sales customers? VAST majority is done by active duty flyers (know tons of Mud Hen crews who did it, for Israel, the Koreans, and the Saudis. Probably fly a few out to Singapore to as they accept delivery). Interesting and fun trip usually, but they always told me the highlight for them was "that new jet smell!"