There is a vast difference between fecal transplants and the "probiotics" that you find in the healthfood section of your local store.
Yes, that's true. The former is for use in emergencies. The latter is what you use to avoid getting into an emergency situation. Because as it turns out, your intestines are possibly the home of your immune system in a very real way. Your gut bacteria turn out to be very important to immune defense, and what you eat has a direct influence on your gut bacteria. In particular, eating a lot of sugars feeds the harmful organisms and permits them to outcompete the beneficial ones.
The key difference is that one has been proven to work in rigorous and repeated scientific study, and the other has not.
Yes, that's what the FDA says about anything that hasn't undergone tests which check their particular boxes, whether they're good science or not. I have looser standards than they do. Also, I don't actually trust them. In this case the EU health cocks say the same thing, but that's no different really.