Can I sprint while flying in Creative Mode to move faster?
Yes, as lunboks explained, you can sprint-fly by sprinting and then flying. I ran a couple tests, and it doesn't actually make you go faster; count in the longer setup time and it's slower.
I've put up a 100m course, where I fly straight for 100 meters. I get myself a few meters for getting a running start, so that this doesn't skew the results. Here's the result. Make sure subtitles are on.
For those who can't view YouTube: Once you remove the setup time, the speed is just about the same. Flying without sprinting oddly wins by a couple tenths (9.33 vs 9.38, roughly), but I just put it to a problem that exists between my monitor and my chain (was I perfectly centered? perfectly aligned? did I avoid swerving at all? etc.).
Yes. If you start flying while sprinting, you'll be sprinting in the air. However, you can only start sprinting while on the ground.
You can verify this by paying attention to your field of vision — both flying and sprinting separately increase your FOV, and if you stop sprinting in mid-air, you'll notice it.
I'm not sure if this actually makes you go any faster or if the flying speed simply overrides sprinting, though if it does, it can't be much.