Black sharpie unless the hat is black then use silver sharpie

Most famous people use Sharpie Marker, so I'm guessing that Taylor Swift signs her autographs with that same maker.

I'm sure that the website, because they do this for a living, have access to celebrities and can ask them for autographs anytime, but because Marilyn has been dead for 50 years, I'm afraid only the autographs that currently exist are authentic, but there are some that copy her signature.

Can putting sharpie on your hair damage it

You can get sharpie off of anything by tracing wherever the sharpie mark is with an expo marker.