My wife didn't have the patience to wait for an answer on the stylus question, so she removed it to find out for herself. Here's what we found out:
1.) The needle trick.. brilliant! The whole process took a couple of minutes. Use the needle to slowly peel back the plastic. Start at the corner (obviously).
2.) That screen protector is VERY thick and strong. No wonder the stylus input wasn't being picked up properly.
3.) Screen: MUCH BETTER. There is no question. Shouldn't even be up for debate. Right before we took this off, we were looking at photos. More clear, brighter.
4.) Touch input: Dramatically better. I have two stylus (styli?), a cheapo and an expensive one, both work great on it now. Even light strokes with the pen register now. If you need to apply a ton of pressure to draw straight lines, then you need to remove the plastic. Try with Draw Something and SBMX. So. Much. Better.
I'm sure there was a reason Sony put this piece of plastic on, but I feel I'm finally using the tablet to its potential. Pro far outweighs con.
If not, not too scared of scratches?