1) Zod is dead, after Superman snaps his neck you can see the Heat Vision in his eye slowly fade away to inanimation. And Seriously...? This looks happy to you?
He just killed the last of his heritage (not including himself). That guilt has to be weighing heavily here especially with the theme of insider vs. outsider displayed here. Additionally, realize that this Superman is not a finalized concept, like the comic books he's a hero starting out, so he doesn't have an finalized notion of his morality. Perhaps the experience of killing Zod leads him to adopt a no-kill policy, just as Batman adopts a no-kill policy because of his parents' deaths and the pain he felt from their murders.
2) How could Zod kill himself when you clearly see the force of Superman's snap breaking his neck? Additionally, how is it that when Zod used Heat Vision countlessly, that his neck didn't snap back? Sounds like a poor excuse to make up for the reality that Superman killed him. Moreover, It was clear that Zod was interested in killing, and struggles in moving his head so that he could kill the family. The problem is that Zod was genetically bred to be a violent man, Superman could've done everything from a rational standpoint (talking/negotiating) and and it would be ineffective...we're dealing with a genetically manipulated killer.
3) Seriously...? Why would they hint at that being a manipulation and not at least hint Lex Luthor? (I don't mean Lexcorp-style easter eggs, I mean actual dialogue to hint Luthor behind the scenes). No offense, but that's a horrible ending vs. what MOS showed.
No offense, but you're really reaching so that you can justify the need to not have him killed, but this is an entirely new Superman. And I personally believe that in the context of the situation, this was called for and righteous, otherwise even more guilt falls on Superman for getting people killed instead of stopping Zod.