That is also true yes, the earth is moving around the sun at an average speed of 29.78 km/s. And the sun is moving around the galactic centre at roughly 220 km/s. So you will move relatively far over 12 hours.

Technically, it does. But by such a small amount, we can't even measure it with the most precise tools we have. This is because the earth is very heavy compared to us, so the jump has a much bigger effect on us than it does the earth.