How remove old nail polish from the carpet?
Any non-acetone finger nail polish remover will take that off and not hurt the carpet. Take a paper towel soak it down a little and wipe it off. Try to keep the area contained that you rub, at first it will look like you are smearing it around, just keep changing paper towels with a new one until stain is gone. You need to change your cloth several times so you're not sliding polish over a bigger area. When done a liquid dish soap will get the smell out of the carpet.
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Nail polish remover will get it out of the carpet. You can also try a few different kinds of carpet cleaners to remove the nail polish, that might work.