In terms of S8 ...
I believe that more than one battle will be fought against the undead army, but agree that the penultimate battle will happen during the second last episode.
In terms of theories regarding Bran and the Night King, going by the books and GRRM may lead you astray and D&D may have their own plans to please the audience and we may just have to wait. I believe that the three eyed raven and the NK have to remain two separate entities... good vs evil.
Happy Ending ... I think that a lot of characters are going to die, just who remains uncertain.
I could go into more with the abundance of theories but that would be of no use.
VBB
You could very well be right.
I'd be surprised if the Night King is still battle-ready by episode 5 (penultimate episode, or second from ultimate, in a 6 episode season), but I'm usually wrong.
I hope there will be enough time for conflict to be resolved between Lannister/Golden Company forces and team-Targaryen. This assumes that Yoren doesn't screw Cersei over somehow, which I'm half-assuming he will (Golden Company isn't in the business of reneging on a contract, but is the contnract to Cersei, the Iron Bank or Yuron - not sure who physically has the gold).
Here's GRRM's 3-page outline to Harper-Collins from 1993:
http://www.businessinsider.com/game-of-thrones-was-supposed-to-be-a-trilogy-2015-2
"Bittersweet" to me means good probably triumphs over evil, but at great cost.
My money would be on House Lannister and the Night King falling, and at-least Arya being around from team-Stark. I have to think either Jon (on Rhaegal) or Daeny are going to need to sacrifice themselves in-order for the other to earn the Iron Throne. I think Daeny dying would be better, only because Kit Harrington would be awesome at brooding on the Iron Throne.
But even that sounds tropey, and if GRRM has anything to do with the ending, I mostly assume he'll attempt to subvert traditional-fantasy themed conclusions.
I do hope the show gives us enough post-war storyline to satisfy us, as we know spinoffs will be prequel stories, not sequel.