--yes. To everything you asked.
Those who have experience healing--I am one of them--often did not know it was healing except in long-term retrospect (a good reason for keeping symptom journals, by the way, so patterns can be seen over time). During the process, the attempt of nerves to regrow and reconnect can be painful, and can also result in a lot of unusual parasthetic sensations as the nerve growth cones find their ways through and around other tissues. Many have said that this feels not unlike the original neuropathy attacks they've had, and they only noticed in time that these symptoms (very) gradually lessened or even eventually disappeared. At the time, though, it was often impossible to distinguish this from "flares" or "exacerbations" of symptoms, which might well feel exactly the same.
Our brains have little reference for how to interpret erroneous nerve signals--and that includes the signals that come from nerves attempting to regrow and reconnect, as well as those that come from nerves being damaged. So pain, tingles, zaps, electrical current sensations, pulses, feeling of touch that don't correspond to anything actually touching an area, weird skin tightness feelings, and so on--have been felt in both scenarios.