What are these marks in my paint amd how to fix...
 

Were on the roof of the car when I bought it. Are they water marks? What's the best way to correct them?
https://cimg7.ibsrv.net/gimg/rennlis...9f85cabc7c.jpg
https://cimg6.ibsrv.net/gimg/rennlis...4d08378ede.jpg

If it is a metallic color and thus a basecoat/clearcoat finish, it is probably the clearcoat failing. But the best approach is to start with the least invasive polishing product and see if they can be removed. There is a chance something "spilled" on your car and can be removed. But stick with polishes, not sanding. The attached link is just one example of what you could use,

https://www.summitracing.com/parts/m...waAv8XEALw_wcB

Need a little back story

when did you notice them?

In the fall when I bought the car. PO said he didn't know where they came from, which may or may not have been true. Paint is generally in good condition on the car except for these spots on the roof. Hoping the polish suggested works. Main reason I'm asking about this is I've read the paint on these cars is pretty delicate and can't take aggressive polishing.

As a general statement, any 30 year old clearcoat is going to have suffered from the ravages of time, especially UV light exposure. Porsche most likely used BASF/Glasurit products, which used superior base chemical stocks versus cheaper suppliers. But yes, go easy on it. I think you'll know pretty quickly if you can fix it . Start at one edge of the blem. If it recedes like a melting ice flow, you might be in luck. If it gets bigger at the edge, it's probably a clearcoat failure.