(1) I'm hard pressed to pick a single app, as really the multitude of media options is the primary thing I like about the Kindle Fire. Reading books, magazines, newspapers, watching movies/TV, and sharing on social sites is what makes this a nice device. But having Netflix and a 7" screen are probably one of the apps I'd put up there as a big one (although Prime could be there too depending on how good the library is). I have a busy job and 3 kids so most of my "personal" time is the 2 hours of train riding a day, so access to media (granted, Netflix would require me to use my hotspot, but so be it) is a big thing.
(2) Honestly, the feature I like the most is the color. Most of the books on my current Kindle are technical books and color for the graphs and illustrations would be a nice improvement over the grayscale I currently have. I'll give up the readability of e-ink for that (and let my daughter have the e-ink Kindle as she just reads fiction).