Potted plant left ring and hard spot on carpet, also nail polish stain?

I'm moving out of my apt in about a month and I have this ring in the carpet where I once had a potted plant. The pot had been leaking apparently, when I removed the plant there was the ring plus the carpet there was discolored and hardened. Any tips as to how to fix that? There is also a nail polish stain, google turned up a few different solutions to that. Vinegar, baking soda, and shaving cream, I don't have time to try them at the moment, so in the mean time I'd like to know if anyone has tried something that worked well. Not sure what the carpet is made out of specifically if it matters. The color is brown, and I'm pretty sure its somewhat old...nearly all the flooring in this apt is really outdated :P