First off, great looking Boxster! But then I'm a bit biased.
On issue #3, the hard start, I'm going to take a guess that the last time you had started it was just to move it into the garage, then shut it off. Starting them for just a few seconds floods them. If that's what happened then it's very common and not related to any malfunction.
#2, I've never tried it, but I would think that using a polishing abrasive like the headlight stuff might make the window worse. I'd try it on a small spot first. They make new retrofit tops for the earlier Boxsters that have a glass window. Highly recommended! I love mine, and can't believe I put up with the plastic window as long as I did.