1. By now, every single nebula in the game is likely to be thoroughly explored. So you won't be doing much actual "exploring" once you get to each nebula, just sightseeing.
Which is pretty much what the OP wrote about, visiting nebulae to see the sights.
About that part about nebulae being thoroughly explored, I wrote
this post at the end of last year, and judging by some quick looks at EDSM data since, the point that there are still undiscovered systems to find likely still stands.
As for doing a route that visits all large nebulae, that's an interesting question. On one hand, you have 245 waypoints to visit: on the other, for the purposes of visiting them in Elite, you don't need a perfect route at all. A ship with a jump range of 40+ ly (which only five ships can't reach) should be able to get from any waypoint to any other, and since all of them should be within the 20 kly limit of the in-game route plotter, the systems in-between don't need to be considered. Plus you don't need an exact solution to the TSP here, approximation should do well enough. Finally, this being Elite, you don't have to return to the starting point, which is also a significant help. (You could restrict the end point to Colonia or perhaps Sagittarius A*, but pretty much any waypoint should have a public carrier with a shipyard within 5 kly anyway, so any end point would also do.)
Oh, and there's also that most nebulae are relatively close to each other, and there are only a few outlying ones that are alone (as in, not in clusters of several nebulae): that should help too.
So yeah, I think that coming up with a good enough practical route should be entirely doable. There's even that
EDJP can create and optimise routes, although I don't know what algorithm(s) it uses for that. Could give that a go too, see what it comes up with.