If the Northern Hemisphere spins counter clockwise, and the Southern Hemisphere spins clockwise......?

It's not that earth spins differently, it is that your observation point is different.

Both hemispheres and the equator spin the same way.

Counter clockwise if you are looking down from the North Pole. Clockwise if you are looking up from the South Pole...

So to answer the equator question...it depends from where you are looking at it.

If you look down on the N pole, the N hemi spins CCW. If you look down on the S pole, the S hemi spins CW.

So the equator goes CCW when looking down on the N pole and CW when looking down on the S pole.

You really need to get a globe and do some W to E spinning while looking at the globe from the N and from the S. You'll see that CW and CCW are relative to your perspective.

This depends upon the location of the person who observe.