The display is Gorilla Glass and thus very hard to scratch. Active pens have been commonly in use for more than a decade on Windows tablets, and they do not damage screens, even with heavy pressure. The pen nibs are made of nylon, and eventually wear down (that's why Samsung provides spares). These are softer than the tips on the styli used on old Windows phones.
I don't think you'll need a screen protector, but I doubt it would interfere with the pen. And yes, the pen works everywhere your finger works.