For a hundred thousand years.
However, the longer it lasts, the lower the intensity of radiation produced.
You can't even safely assume that we will have political stability over the next couple of hundred years. Whether it takes a thousand or a million years either period is so long that is is insane to believe it could ever be stored securely.
Yes, but it has a much larger risk: the risk of tens or hundred of thousands of people getting radiation poisoning, and the region becoming inhabitable for years.
Plus it creates nuclear waste, that is not mere pollution, but extremely toxic for thousands or years. Not to mention the consequences to be had with a nuclear plant in the hands of the wrong people (terrorists and such). With a coal plant, not that many...