1) Melisandre said she will return to westeros to die with varys. What does this mean? Will it be happening soon, and be important for the Winterfell battle?
Probably not. I don't see Varys getting killed in Winterfell, they probably die of old age somewhere in King's Landing much later on after all the chaos.
2) Is it possible for this battle to end with a night king victory? This is GoT after all
Possibly, but then you have all the building of characters all for naught. I also don't see the Night King's post battle life taking up three episodes, 2 of which are 80 minutes. I don't see it happening.
3) Someone pointed out that the night king can't be seen or heard in the cliffhanger. Will he be there, or will he be headed elsewhere to gather more men? If this is true, I can see Wight Cersei (Night Queen) and the Night King coming, and then Tyrion or Jaime will kill her Wight form. THAT would be an insane twist, as well.
Cliffhanger didn't want to give away too much from the fight, as it would ruin the fight. He may just show up late to fuck shit up and freeze all the troops once they're out on the field, then fly in and swoop up Bran.
4) If Bran dies... does the world end?
I don't think so, as they brought up using Bran as bait, and how killing him would just erase all of humanity's history from that world. The memories of the three eyed raven seeing everything (past/present) would be erased, thus all history of humanity forgotten. Presumably they (white walkers) would destroy all books as well.