- Jon and Dany are ambushed by the Night King and his ice breathing dragon, only for him to disappear within a few seconds. Again, it just seemed random and was another thing that happened that didn't seem to really matter
If you watch it again, I think it appears that the NK baited Jon to take him and Dany and thereby both the dragons away from Winterfell. He flies close enough to get Jon's attention then fecks off into the snowstorm knowing full well he'll be pursued, and he deliberately took them into where the storm was more intense to give him the best chance of taking out the two dragons and to make it harder for them to navigate back towards Bran/where they need to be. That's how I saw it after I re-watched most of it this morning anyway; I may be mistaken but I also recall that the other White Walker leaders march through Winterfell shortly after the NK baits Jon and Dany away from there, I'm guessing they did not share the NK's invulnerability to dragonfire.
I concur with most of what you said though. I found it most disappointing how the NK was killed in one moment and that was it. I don't know what I wanted, but we never got the intense showdown involving him that we anticipated. Like when he was smothered by dragonfire, I'm sure everyone watching it knew he'd emerge unharmed as that would be far too much of an anti-climax for him to be taken out so easily. Yet that's basically what happened in the end with Arya.