There are pretty straightforward answers to two of those three questions. First, running lights (red port, green starboard) weren't introduced until well into the nineteenth century; I've never seen a representation of them before at least the 1850s. Second, she might conceivably have had one or more stern lanterns (they were in use in the early nineteenth century), but I can't recall seeing any painting or drawing that suggests that she did. Third, it would be normal to have a few lanterns burning on the lower decks at night - in the officers' cabins certainly, and probably here and there on the gundeck and berthdeck. But almost certainly not on the spar deck (the weather deck). The only lights you'd normally see there would be in the binnacles, to illuminate the compasses.
Apart from the stern lanterns (if any) there certainly was no "lighting system." Things that needed to be illuminated would be lit with portable lanterns; that's it.
Hope that helps a little.
Incidentally, I was interested to read your earlier post about your long-time relationship with the Mariners' Museum. It is indeed a great place. But with regard to my having left it, I think all I'd better say is that the grass always looks greener on the other side of the fence. I've never regretted leaving.
Later edit: I got curious about the first appearance of navigation lights, and looked them up on Wikipedia ( http://en.wikipedia.org/wiki/Navigation_light ). Looks like, as I suspected, they made their first appearance on board American steamships in the late 1830s and sailing ships a decade later. If I remember, right, the big model of the whaler Lagoda in the New Bedford Whaling Museum has red and green lights in her mizzen shrouds. That's the earliest example I can recall seeing.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.