I am absolutely sure that humans can feel emotions in a dream. I've experienced some of the strongest anxiety in my life during nightmares. Sometimes the emotions were strong enough to persist in the real world - I remember once seeing my father at the lunch table and feeling my metaphorical hackles rise, preparing to hurl an argument at him - and being confused why I can't come up with a good argument, until I remembered that I'd just dreamed the heated argument we'd had, and my feeling mad at him wasn't due to any cause existing in waking reality.
I have also experienced sensory inputs which were definitely present in the real world and got seamlessly incorporated in the dream, e.g. the sensation of a full bladder, or of being cold. So I'd think that in general, sensory inputs from the body can be felt when one's sleeping and dreaming. Also, I think that it is possible to dream some sensory state which doesn't have a cause in physical reality, just like it happens with emotions (but can't remember an exact dream where this happened).
On the other hand, one of the most overused tropes in fiction is heroes who pinch themselves to make sure they aren't dreaming. I find this quite strange. If my understanding of sensory input in dreams is correct, a pinch shouldn't be any proof - a person could feel the pain while dreaming, and keep on dreaming. Maybe the logic behind that is that pain is such an important signal, that when it is felt, even if it was caused by a dream, the brain will awaken the body to prepare it for response to a danger - so pinching oneself in a dream will lead to dreamed pain, which will lead to an awakening.
I have never felt compelled to pinch myself to test if I am dreaming - certainly not in waking reality, and if I did it in a dream, I must have forgotten that dream, which means that it can't have worked. I have sometimes surfaced of a dream enough to notice that I am dreaming, decide either "what a lovely dream, I want more" or "dumb dream, I want something more pleasant" and continue dreaming without waking up, and sometimes I can really take decisions at that point which influence the story of the dream. So it is plausible that a person could decide at such a point that they will now pinch themselves, and dream that they are doing it. But will the resulting pain be enough to wake them up? Or will they experience no pain at all from a "dream pinch"?
And is there any way at all to make a dreaming person experience pain - either from external stimuli, or from a voluntarily dreamt pain stimulus like the pinch, or from an involuntary dreamt stimulus like the dreamer dreaming that a car is hitting them? What happens when a dreaming person experiences either of these three?