Cleaning is easy. A floor cleaning solution for vinyl = easily found anywhere. The scratches are probably permanent but should "disappear" (visually) once the proper wax/sealant is applied to the VCT. Find the manufacturer's preferred/recommended sealant/wax and go ahead and apply. The scratches will most likely minimize once the product has been applied.

When you contact the manufacturer re: wax/sealant, you can also ask about how to remove/reduce the look of scratches. They will have the best answers for their product.