Is the maximum of a single stat 1/3 of total possible stat increase? if not, how much?
Correct. If you have a maximum potential of 63, then each stat's maximum potential is +21. If you have a maximum potential of 99, then each stat's maximum potential is +33. Etc.
Is it possible to achieve the maximun of a single stat using reputation only? If not, what is the max?
My understanding is that post a certain level (I think it's lvl 20 in Avalon, it might be something similar in Vampire Wars), you can only use reputation to increase each stat by +1. Thus even though your maximum potential might be something like +83 per stat at lvl 50, in reality you can only reach +70 per stat with reputation alone. You would need domistal/gems to increase beyond that.
I made these numbers up since I don't have an actual hero in front of me. My rule of thumb is to add +20 to the hero's level and that is the maximum potential you can reach per stat (without gems/domistal).
I might be wrong about this though. There doesn't appear to be much concrete information on the enlighten system. Some people have posted methods to best enlighten heroes, but honestly I think the random number generator is more often your enemy and just wants to suck away your hard earned points.