Depends on how it's done. If they do it the dirty bomb way and winds are unfavorable, sure it could happen, but they'd have to basically set off their own nuke in the plant to make a cloud that would significantly affect anyone outside Ukraine. If they just let it melt down, probably not but it'll wreck the plant and the area immediately nearby.
Still, couldn't hurt to pick up a pack or two of iodine tablets just in case.
No, they haven't. China got hit just as hard in the 2008 recession as most western countries, and they've been robbing Peter to pay Paul ever since. Eventually Peter gets his due, and China will suffer a serious economic setback. You're starting to see signs of that now. China right now is Japan in the early 1990s. Everything from the inverted population pyramid to the looming debt crisis points to the next decade being very flat for China, and their wolf warrior diplomacy hasn't made them the kind of friends that could help pull them out of it.
That's not to say that western capitalist markets couldn't stand to be significantly more regulated, because they absolutely desperately need more regulation around safety, negative externalities, and anticompetitive behavior. But claiming that China hasn't experienced recession is preposterous. They're too economically coupled with western economies to not suffer alike as recessions hit.