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Question #1: Could this setup really produce a fairly loud, high-
pitched noise that can't be heard from inside (just the other side of
a drywalled, non-insulated garage wall)?

Yes

Question #2: Since I can't hear it from the inside, can I rule out
the exhaust fan and conclude it's a whistle from rushing air moving
through the vent hose?

No


Question #3: Would moving to a rigid vent pipe or a different outlet
cover help with air/whistle noises?

Very possible. Noise does some funny things. A few years ago our company
went from two to three shifts. A neighbor about four blocks away complained
of the noise of our compressor. He came home late so the second shift never
bothered him, but now the third shift did. The noise traveled up the river
by the plant to his house where the harmonics drove him nuts. It was just
a matter of changing an air intake in this case. It did not bother him
standing near it, and he could not even hear it across the parking lot, but
up stream, it was very noticeable.

My guess is you have a similar situation. I'd try changing the flapper vent
first. You may want to wrap some foam rubber around it where it passes
through the wall as that may be setting up some vibration or acting as a
sound board.