No more than any other form of cooking. But you are not going to eat raw meat anyway, are you? It may not be the best way to cook something like fresh spinach but you should still be getting nutritious food. Even as the proteins break down they are going straight back into the braising liquid.

I had not heard that, but would think it would be a similar situation as in any long, slow braise. It's just an extended version, really, of stewing or braising or pot roasting in liquid in the oven on low temperature, or simmering on a stove-top for several hours. If anything, I'd think the gentle heat from the slow cooker would be more likely to preserve the "good stuff" than not. But I'm not an expert.

That said, I wouldn't worry too much about it. So long as you're starting with good, fresh ingredients, and not using loads of pre-processed food in your recipe, you're getting loads of beneficial goodies in your finished dish.

I have never read such a thing, do you have a citation for such 'information'? A quick google search only turns up crackpot references.

In general cooking at all will destroy some nutrients in vegetables. It doesn't mean that you don't still get many nutrients. But cooking makes other nutrients more available in some foods, like carrots and tomatoes. I haven't heard that 'slow cookers' or any kind of slow cooking, like braising is any more a culprit of robbing nutrients than any other type of cooking,