At 20:10 'nearest' counts the shortest path following the rules of the action in question, meaning if an enemy attacks the nearest opponent with a range attack you do indeed count diagonal, but if the enemy action is to move to the nearest opponent then Rook would be closer than Zeke!
The summon change has got to be one of the worst things about 1.2 as it only affects the players and only if an enemy directly attacks the summon. So any other source of damage dosen't hit the summoner. It also doesn't work the same way for enemies as they are disconnected from damage the summon takes. I understand they needed to balance the way summons worked as they were to powerful in earlier builds, but it should at least make sense. Honestly, 1 summon per player and taking the summon tokens away would have been better than what they changed it to and our play group house ruled it to this. Only other option would have been to connect enemy summons to the summoner but that would trivialize a few encounter.
It's possible there are story-related triggers that unlock upgrades (I haven't played through the whole story), but otherwise yes, that is the only way I know of that you unlock an upgrade.