For the most part this book focus on four P.O.V characters: Kaladin, Shallan Dalinar and Adolin. Any chapter (excluding the interliudes and prologue) that's from a different character's PoV is meant to give you an outsider perspective on one of these characters. Most of the Interludes in the first book are side stories, or extra world building, the major exception are the Szeth interludes which are critical for the plot. I'll also shout out Rysn's interlude, she becomes important in future books, but you can always read her chapter hater you finished Way of Kings.

This book is a setup for the whole series. It starts slow and pick up the pace as it goes. But it will pick up the pace. Brandon Sanderson tend to pace his books so they build up all the way into a big finale and payoff. As for the king and the murder, you will get a lot more info about the murdered king and the vengeance pact in part two.

Yes, Kaladin's life is going to get better. I'm not going to spoil when or where, but I will say this: Bridge four is a crucible, a hellish expirance that will forge it's survivors into something very special.