I'll be seeing BvS this weekend, in spite of how I felt about MoS.
I'm glad that you managed to gleam this from the film but I just couldn't look past the contradictions. I couldn't accept that Jon Kent believed so strongly in his ideal that the world wasn't ready for Clark that he was will to sacrifice himself in the most unnecessary way possible to prove it. I couldn't accept Zod's really crazy motivations to terraform the Earth and kill everyone (for what reason again?) and I couldn't accept why as opposed to doing the heroic things you described Supes didn't simply take the fight somewhere else like every superhero has done ever!
Superman did not have the option to take the fight elsewhere, the kryptonians were engaging earth forces in the Kansas fight and abandoning them means they all died, whether or not he succeeds in luring Zod personally to a wasteland somewhere. That's also the fight prior to them discovering that the Codex isn't anywhere near Kansas, and they may well have turned the city upside down looking for it. In the metropolis fight at the end he can't go anywhere because Zod's motivation at that point is the cause as much destruction and death as possible out of spite for losing the world engine, not to pursue or capture Kal.
Pa Kent is probably the most singularly controversial story decision of the film. He was a sacrificial lamb to a plot point, that humans weren't ready. The movie shows he was wrong, but I don't see why that makes it dumb that he believed in his own opinion with conviction. He thought he was protecting his son. You could make a nitpicky case that if he zoomed in and out fast enough nobody would recognize him, possibly true, and I'll call that a failure to justify it correctly in mechanical terms. The overall character decision I don't think was problematic though.
Zod wants to terraform the earth to make it the same physiology as Krypton because his purpose in life was to safeguard Krypton and apparently he's interpreted that to mean recreating it is the next best thing. He does not value the life of the humans, nor does his band of followers place much value in such things. Faora says lack of morality makes them stronger, but really that was a stupid line of dialogue because they do have a morality, it just isn't a moral system that values humans.
The film's themes were just unnecessarily dark and grim (hence the grimdark) for a Superman movie to me and seemed to be that way all for the sake of being different and edgy. For every thing that I really loved about MoS (Krypton was the best depiction ever, I could have taken an entire movie of that) Snyder would do something stupid that I hated and took me out of the film. I really wanted BvS to be great but it seems like the decision from the creative team was to take what little joy there was in MoS and make it even darker. Batman actually should be really dark and edgy, Superman... not so much.
The movie was on the dark end of superman stories (not the darkest by comic standards, but the darkest of the films thus far since everything prior was at the extremely light and fluffy end), but in an absolute sense was not particularly dark. It had fewer quips than most of the marvel films but tragic childhood loss, alien attack causes lots of damage, hero saves the day is a standard comic book type story.