They are pretty much interchangable. The difference in tense makes little difference for some expressions. . The second one has no sense of duration; it is instantaneous, so better to use when that's what you mean.

Pretty much 100% interchangeable. The only very, very subtle difference that I can think of is that "How are you feeling" has a slight implication that you know how they felt a short time ago, and you want to know if there's been a change. However, even in that situation you would still be able to say "How do you feel?", and nobody would find it odd.