Daystrom Institute

This also struck me as being pretty strange, but I think everything here can be weaseled around:

'at the edge of the sector': The Vulcan system happens to be at the edge of the sector it is contained within, sectors being vaguely defined chunks of space laid out fairly arbitrarily.

Surveying the moon: The ruins are well known and well explored (our heroes seem familiar with them already, for instance) but this weird energy vortex is new, strange, and merits a starship crew to investigate it. It's not the first time they've sent Pike specifically to investigate a weird energy source popping up somewhere.

I kind of like the idea that Vulcans' control of their emotions is a genetic trait. It doesn't seem too far-fetched, since Vulcans already have mental abilities humans don't, and it gives a bit of an in-universe reason for why Star Trek writers seem really inconsistent on whether Vulcans have emotions or not.

I think Vulcan brains are fundamentally different in their ability to (almost) completely block out emotional reactions, but with those barriers lowered they have significantly more difficulty keeping themselves together than humans do. I am told that a human who tried to go "full Vulcan" with their emotions would mess themselves up pretty badly, but Vulcans manage a functional society of mostly decent people doing that.

Spock, therefore, would have found himself experiencing less overwhelming emotional urges than he experienced in his occasional moments of lost control, but with none of the vulcan-specific mental barriers he was accustomed to leaning on he had little choice but to roll with them anyway.

If those Vulcan mental barriers are variable in effectiveness between different individuals and different emotions, that would also present a needlessly technical explanation for why various Vulcan characters fall into obviously emotional patterns while maintaining very Vulcan outward behavior in other facets. Captain Solok and his racist vendeta as an obvious example.