On Cortana's "Death"... You do realize that there are 2 more games, right? After the credits, (Spoiler Alert), we hear the voice of the Didact. If he could survive that last fight, I'm sure that an AI could survive somehow, especially considering she can fragment herself.
Not to mention lacking Cortana wouldn't be very Halo-ish in the next few games. She'll be back. Use your brain to realize that this is the first game in a new trilogy.
Also, with Graphics and changes in models (Like the Jackals), it only make sense for their to be different appearances considering a new company is creating the games. A lot of the guns have different skins and features as well, if you haven't noticed.
Also, Chief was teleported by a fragment of Cortana using Forerunner tech, which explains why he didn't explode.
A good story has drama in it. If everyone is kept alive, then things get boring.
Also, please learn how to use proper grammar.