The plane on a treadmill one has seemed straightforward to me. Lift is caused by the air moving over the wing and the obvious intent of the treadmill in the thought exercise is that the plane is only moving relative to the belt, so there's no opportunity for lift (no air flowing over the wings). Any other interpretation seems disingenuous.

The one that made me scratch my head for a while is the bicycle on the treadmill. People generally know that it's easy to stay balanced on a moving bicycle, but hard to balance on a stationary one, so is it easy or hard to balance on one that's on a treadmill?

A lot of people think that the stability of a moving bicycle is caused by the gyroscopic effect of the spinning wheels, but that turns out to contribute relatively little compared to the force of a body leaning one way or another.

What actually makes it easy to keep a moving bicycle going straight (or what contributes the most) is that the design has self-correcting steering. When you lean to the right, the shape of the forks causes the front wheel to point left, and vice versa, keeping you going relatively straight as long as you have some minimum amount of forward motion.

And since that forward motion is relative to the surface the tires are on, it works just fine on a treadmill. You can even find YouTube videos of people who ride their bikes on treadmills, and it's very evident.