The process probably started before you even got her, or that line is just so bad it doesn't matter what conditions are (and could be better/worse in different batches).
As far as airing out goes, I don't know what makes it help but it does work! My grandma was looking through her stored dolls (stored in a garage out in the Mojave Desert - AKA the place where I got into a 120 degree car once) and noticed one was sticky. Probably from plasticizer leak but she had no way to know that. She gave the poor thing a quick wash and leaves her out of the boxes now. The stickiness went away and hasn't returned so far.
I think once plasticizer leak starts you're out of luck with customs. Unless you want to wait years for the process to finish and the pony to turn rock hard. I don't know how well those ponies accept paint and sealant though. I imagine rehairing would be a huge pain, though I don't know for sure :P
I would call plasticizer leaking ponies dangerous, to a degree. I'd never allow a child or animal near them. But I don't think mild touching (enough to clean them off etc) would be harmful to an adult. Just gotta use common sense - wash hands after, don't lick em, etc.
I would absolutely NOT introduce any more chemicals to the mix, ever. I'm pretty sure nail polish isn't good for ponies anyways. This is a process you can't really avoid. You either have to throw away the toy or whatever (this isn't a pony problem; its a soft plastic problem), find someone else who'll take it, or wait it out.
You can apply baby powder to help soak it up. I have a doll leaking plasticizer and I apply baby powder every so often. I washed her with Dawn, did a thick baby powder coat, washed it off, and now just keep her coated decently inside and out until it stops. It could take years.