Good questions! In order:
1) As far as I know, polarized lenses cut reflected glare, i.e. from water, snow, or cowlings. They do help somewhat with that, but the drawbacks in flying are what has already been stated: Can't see through heated windshields, can't read some LCD screens. I do think there is a reg against using them, but I'm not positive. I used a pair once, flying freight, and they were a huge pain in the a$$ when compared to other good types. So, since they are a pain in the a$$ in certain situations, I can't think of a good reason to pay extra for the priviledge. MHO.
2 and 3) Get a lens color that enhances contrast/color, like the Serengeti or the Oakley Gold Iridium (i.e. brown-ish colored lenses). The Fire lens may be good too, (not sure though) but I think it allows more light through and would not be dark enough for me. Try them out. Have the sales girl walk outside with you while you compare them directly to each other, looking at clouds and sky. Hold them up to the sky, next to each other. The Ray Ban G-15, while a standard for decades, tends to flatten objects and diminish contrast in comparison. You don't want that. As a funny example, I went looking at a used car to buy once, back when I had my Serengeti's. It was a silver car, and the whole rear end of the car was a different color than the front WHEN I HAD THE SUNGLASSES ON! Without them, the colors were identical, and the casual observer would never known the car had been severely rear-ended at some point in its life. I asked the seller to explain it (he was the first and only owner), but he still pleaded ignorance until I made him put on my shades and look for himself. He quickly 'fessed up! I had my old backup pair of Ray Bans in my glovebox and tried them. The car looked fine! I was amazed. Serengeti's to the rescue!
It's a balance between being dark enough and too dark to wear when cloudy. I think being able to wear them even when it's overcast (not dark overcast) is a great advantage because it really does make your depth perception and color discrimmination better. Translation: clouds, traffic and terrrain take on a whole new life. So does Autumn.
4) Yes, altitude makes a big difference. It's not too noticable at low altitudes, i.e. 5-10K ft, but it is still there - just to a lesser degree. In the Air Force they issued Randolphs, which seemed OK until you noticed guys walking around with sunburned eyes after flying big jets all day. Nobody really made the connection back then, nor did I because I didn't know any better. Now I do, so I'll happily pass on my experience to anyone who asks! BTW, I still have my issue pair of Randolphs, and I still wear them on occasion (not flying) when I want a different look. Just a nostalgia thing I guess.
OK, one last item. Not a factor for you yet, but maybe in the future: If you plan on pulling any serious G's, find something lightweight or has good ear hooks. Nothing worse when maneuvering hard than to have your shades go sliding off your sweaty head and nose. Don't worry about it now, that'll be for later...