There are 2 things about the movie that I still don't understand or have seen anyone explain very well.
1)Why does Spock feel ZERO need to fix the time line? He is the only one that knows about the "Guardian". He knows about the "sling shot" idea. So he can easily fix it. So why does he feel zero responsibility to fix the damaged time line? Billions of lives were lost. His entire life he says "I am a Vulcan" but shows no loyalty at all when his home world is destroyed.
Because he knows "the timeline" isn't damaged, and doesn't need to be "fixed". His original timeline is still going on, exactly as nature intended. Unfortunately, Spock isn't in his native timeline anymore, but is in an "Alternate Reality", which, for all Spock knows, is also proceeding exactly as nature intended. To disrupt the established past of this new reality would be presumptuous, arrogant, pointless, and potentially dangerous. To go back in time and alter this new timeline wouldn't necessarily "fix" it, but might well result in yet another "Alternate Reality". So rather than disrupting the established history of this Alternate reality, Old Spock is content to merely watch this new reality as it unfolds, and perhaps, at time, use his knowledge of possible future events to help guide this reality, strictly "in the now".
Uh, no, Nero does not have all the technology to back up his claim. Rather, he doesn't have the technology to stop the supernova from occurring. That tech is in Spock's ship. Nero's ship does have advanced "Borg-based" tech, but all that would prove to the Romulan high council is that he has an alien ship, which doesn't really prove he's from the future, or has future knowledge.2)What exactly was Nero doing for like 20 years after he went through the black hole? I mean why not go back to Romulus and warn the government and the people. He has all the technology to back up his claim of the impending doom.
Which is why Nero must wait for Spock before taking action. He needs the red matter, so that he can simply save Romulus, without having to convince the council of anything. He plans to simply do it.
So what was he doing all those years? Some say rotting in a Klingon prison, but that never made it to the screen. Based on what we saw in the movie itself? You guess is as good as mine.