Is it possible to tell if the current floor is solid or engineered hardwood?
You need to find an area where you can inspect the side of the boards.  If there are floor registers, remove one and inspect.  If you don't have those, look for areas around doors other areas where you might be able to easily remove a trim to inspect.  Worst case, you will need to remove a floor molding to inspect.

Also height will give you a clue.  1/2 to 5/8 is the typical heights of engineered.  5/8 to 7/8 is the typical height for solid.

And some engineered floors can be sanded once or twice depending on the thickness of the finish wood.