I was wondering, when you do these kinds of videos, are you actually watching the bird itself ...
Both, of course. I try to always face the Inspire so I can easily where it is and also what it is seeing. Not unlike driving a car while also checking your speed on the dashboard.
Is it possible to apply for permits to fly over national parks?
There's no info on permits for this park, which is a municipal park. This from a September press release on US National Parks:
"All permits previously issued for unmanned aircraft will be suspended until reviewed and approved by the associate director of the National Park Service’s Visitor and Resource Protection directorate. The associate director must approve any new special use permits authorizing the use of unmanned aircraft. Superintendents who have previously authorized the use of model aircraft for hobbyist or recreational use may allow such use to continue."