--are not even necessarily painful--they can experience numbness, phantom vibration, sensations of things that aren't there (parastheses), and a whole host of erroneous sensations or lack of sensations.

Much depends on which nerves are damaged--there are numerous types of both small and large sensory fibers, designed to detect different types of sensations--and to what extent (and where).

Yes, it is possible for nerves to regenerate. But they grow back more slowly than almost any other body tissue. One commonly cited figure that is commonly cited is under ooptimal conditions, they can grow 1mm a day. If you think about that, if you'er talking about a fiber to the distal part of a limb, you may be talking years before the full path is traversed--assuming the damage process has stopped, assuming it can reconnect with the original target (and it's likely to take a different path than it originally did, which may re-wire the body in a very different way than previously, if the damage was widespread).