This is the part I'm not getting in regards to Star Trek. Nothing about the space battles in any one of them is "real" at all. They will always be the civil war reenactments, regardless of if they're packed with action everywhere on the screen or if some ships are slowly drifting and firing some lasers.
The director is trying to get the audience to imagine the situation as if it were actually happening. In order to do so, he has several stylistic choices among which to choose.
If he wants the audience to "watch it all unfold", he chooses the outside observer perspective so often seen in earlier Trek movies (and earlier films with battles in general). Today, this is a choice. Years ago, it was a requirement (no feasible camera tech to allow any other option).
If he wants to immerse the audience into the moment by approximating the chaos of real conflict, then the more frenetic style is the one chosen (and has become the default selection). This applies to space battles, hand to hand combat set in the contemporary world or clashing, sword-wielding armies on mediaeval or ancient battle fields. None of these depictions is "real". The goal of the filmmaker is to elicit a feeling from the audience. The immersive, chaotic one is a closer approximation of any kind of real physical conflict (anyone who's been in an actual bar fight will confirm this--it's nothing like in classic movie fights).
It doesn't matter how "unreal" any Star Trek movie (or movie in general) is. What matters is the feeling the director is attempting to evoke from the audience.
As to the firing on the Narada at the end--not too hard to comprehend, really. Once the offer of help is refused (recall that Kirk was hoping it might lead to peace with the Romulans of that time), the next concern is for the safety of the Federation. The Narada might look badly damaged, but it did just wipe out an entire planet (and it had survived a similar black hole before). Why take the risk of them surviving and causing further havoc?
Perhaps it seems out of character, but this situation was rather unusual. Moreover, each of the characters is younger and less mature than the iterations we're used to seeing. They haven't grown into the people whose character is what you remember of them.