I just did my headlights. Suggest you purchase a kit. 3M has a kits to use with a power drill or by hand. The instructions are complete.

The first phase of restoring headlights does make they hazy as in your picture. Looks like you are sanding in one direction, should be sanding in a circular pattern. I suggest masking off around the headlight so you don't damage the paint.

The mark on the paint could be paint transfer from another vehicle if it is not from the sandpaper. Looks like you can easily buff it out with some polishing compound.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas