We are spinning at 1,000 MPH while hurtling through space at over 66,600 MPH. We don't feel this motion and the numbers are pretty crazy to wrap our minds around (especially the Satanic one).

"Speed" is a relative thing. Compared to the surface of the Earth, we are, at least in general, travelling at 0 MPH.

The way you feel rotation is by the Coriolis effect, or the Coriolis force. This force is easily seen on any rotating device (like a merry go round). When you model the behavior of this force in the language of math (what we call "physics") it works out to:

F = m dw/dt

where "w" is really omega. This omega stands for the angular (rotational) velocity. In this framework, we aren't moving at "1000 MPH," we are moving at 1 rotation per day, or 1 rotation per 86,400 seconds, which is actually REALLY slow. Thus the coriolis force is very small, because dw/dt is very small..

If you were to create a merry go round that was 8000 miles wide and set it spinning at one rotation per day, you would feel the exact same force as if you made one 10 feet wide and set it spinning at one rotation per day, which is to say, you wouldn't feel a thing. We have to set up fairly sensitive experiments to measure this force on earth.

The best experiment to measure our rotating planet is a Foucault's pendulum experiment. This experiment not only shows that we are spinning, but because it always comes up with a different result depending on your latitude, you can tell, with this experiment, exactly what latitude you are at.

The results of any such Foucault's pendulum experiment match with the mathematical model of what the behavior of a pendulum would look like if one were to put one on a sphere. This model has nothing specifically to do with earth. It's just the model behavior of a pendulum on a rotating sphere. It just so happens to work out perfectly when one measures the precession of a large pendulum anywhere on the surface of the earth.

If we are spinning this fast, airplane trips going against the direction of the spin should take longer or be impossible.

This similarly completely disregards all physics. I'm not suggesting physics is some perfect thing, or that there is no fuckery contained in physics, science, or any other area of our "knowledge;" however, it isn't all fuckery. When we make models of behaviour, and our models match experiment/experience, our models prove themselves useful. That doesn't make them "truth," but if you are going to present arguments against the conclusions, you must at least address the experiments that show strong evidence against your arguments.

Your "common sense" does not match experience, except by misapplying experience to larger phenomenon. For example, if you take your experience on a merry go round and apply it to the earth, all sorts of reasonable protests arise. But if you appreciate that a merry go round isn't about "speed" but about angular speed, which is something anyone with two different sized merry go rounds can corroborate, then you will realize that your small scale of experience is not sufficient to make predictions of larger scale events, and thus should not be applied to that task.