Wow! Where do you live?

I can guarantee you that there are indeed stars at night, I and billions of others see them.

If the coin spins on a horizontal axis, a gyroscope on the flat side of coin will still be pointing up.

Yes it will, however there will be no 'drift'

Coincidentally this is how the earth moves if you believe it circles the sun and the sun moves as well relative to stars.

It's a not a case of belief, it is something we have proved, the following text is lifted from astronomy.com, however I'm happy to show you other proofs if this isn't satisfactory to you.

Earth’s orbit is huge — some 186 million miles (300,000 kilometers) in diameter. If an astronomer measures the position of a nearby star, and then measures it again six months later, the star’s apparent position against the background of more distant stars should shift a tiny amount.

Observing this would prove that Earth in fact is not stationary. It wasn’t until 1838 that an astronomer finally detected this shift. That year, German astronomer Friedrich Wilhelm Bessel successfully measured the parallax of the star 61 Cygni.

And there’s yet another proof. Imagine standing still with rain coming straight down. To stay dry, you just hold your umbrella directly over your head. As you begin to walk, however, you need to tilt the umbrella “into” the rain, even though the rain is coming straight down. The faster you walk, the greater the tilt needs to be.

As Earth orbits the Sun, we can detect a “tilt” of incoming starlight. English astronomer James Bradley discovered this phenomenon in 1725 by accident — while he was searching for stellar parallax! This aberration of starlight, as it is called, is a result of light having a finite speed and Earth’s motion around the Sun.

Cg