Yes it was an ingredient in a LOT of things.  No there's no need to STOP collecting things that bring you joy... just... don't put them in your orifices and wash your hands after playing with them.    LOL  Use gloves and pretend you work in a museum.

Now if you had some radium items I'd tell you to ditch them quick - by calling the fire dept.!!!   
And celluloid dolls have to be stored carefully because HEAT=spontaneous combustion!!!!

But vintage toys....?  Don't lick them, don't file bits of them off and huff the dust, don't decorate a child's room with them... uhhhh I mean the usual safety precautions to life...

For sticky ponies, I just keep them separate until it's done and they go hard, and don't leave them on painted surfaces. If they're on a painted shelf, put them onto something, like an old CD, or they'll stick to the paint. I rinse them whenever I have a bit of time, or have to move them, to keep dust from getting all over sticky ponies, that's just gross!

Most of my G3 glitter ponies, and my Trickles are weapons now, you could do some serious damage! Twinkle Eyes are sometimes naturally harder, so once she's hardened, she'll just be like most of the TE population! My Masquerade has definitely not started leaking yet, she's not that hard, but she's still awfully rigid considering. maybe they either got too much or not enough plastic?!

Improperly filled moulds seem to be a problem for Masquerade - mine has the same problem! The plastic on her back legs is nearly transparent and super squishy 
Additionally certain temperatures (or a change in temperature) seem to aid plasticizer breakdown in progressing to the hard non-sticky stage. I've bought ponies advertised as horrendously sticky but after a few days in the Australian weather they're all good.

Also, as a side note, I love your Mini Mozzarella avatar! Retro animatronics are awesome!

Your pony isn't "melting" per se, she is leaking plastisizer. Unfortunately, this process can't be stopped once begun. But it can be delayed, if you're so inclined. Thought honestly the ultimate effect of the plasticizer leaking is that the plastic will become really really really hard. like hard as rock. You can curb the browning spots by thouroughly cleaning on the inside with an oxiclean bath, but her condition will never fully go away.

there is nothing """"bad""" about hardening plastic, it's just something that happens. It will take some time though. she will be sticky for possibly months or longer. you can clean her with dish soap reguarly every time you notice her getting sticky.