I've got no idea about ponies, but I've done some decent paintjobs on Airfix and Warhammer models before. First of what kind of plastic are they made of? Acrylic paint should do the job for most plastics, or you can splurge a little more and get some proper model-painting stuff. It tends to be thinner and easier to paint on to plastic. I'd avoid oil or poster paints, I believe they usually clump and then flake off as they dry if you try and apply them to anything over than paper or canvas. I'm really not the best person to talk to about this sort of thing, so if anyone knows that I'm completely wrong (which I might be) then don't hesitate to correct me.
I personally do not know how to repaint figures, but my friend does http://askstarswirl.tumblr.com/ Here's a Carrot Top she made: http://inkeed.deviantart.com/#/d4fkrhl
I don't do repaints but I've seen my friend do all her commissions and stuff in person. Acrylic paint does well on it. I'm not sure if you have to get rid of the color first. I'm pretty sure. Then she puts a glossy finish on it. (Unless the glossy finish was for her custom brushables.)
Acetone apparently? Then you can repaint the whole thing. I'm not for certain but that's what I assume.
Yeah, you could probably strip off the colours with something... Unless the toys are actually made of coloured plastic? In which case you could probably bleach them... I guess.
You can remove the plain coat. Use nail polish or acetone. Then just repaint with acyclic paint and stuff. (Not sure if you need a glossy coat.) :derpe:
