How do get this model to rotate around its center point?

How do get this model to rotate around its center point?

Did you use the Center 3D button on the upper left corner?
https://slicer.readthedocs.io/en/latest/user_guide/user_interface.html#d-view

How to rotate only the model, but not the view.

You can put the model under a transform and use the rotation sliders to rotate the object.

See video tutorial for the solution that @muratmaga described: