Does the skirmish interface for java allow me to get an event when a team is 'out' (depending on settings, commander killed, or all units destroyed or whatever)?

no. the reason is.. i would say, you should not have to know wnayway, but also... it is not so clear when a team is really out, it depends on the mod. some mods, some modes, the team is out when it lost the commander (other units could stay to be taken eg), could be if all units were lost. or if some other requirements are not met. osme others you may loose when you lost a certain ammount of points (think of batlefield), ...
in general, an AI should always produce more, attack, expand, no matter whether the game is over or how many teams there are left on each side. you should rather care for general strenght of your allies, your enemies, which depends on the number of their units, not the number of teams.

When playing against bots on Age of Empires, when I'm razing the base of an AI, I'll only raze until it's dead, I don't have to waste another minute or two razing the whole base. Then I can straight away start to attack another AI instead.

I guess that Spring engine knows when a player is dead? Or not? Perhaps it should! ie, perhaps Lua should tell the engine when it feels a player just died?

Players know immediatly when an enemy is dead, why shouldnt an AI? Its a signal for us to immediatly free up resources expended on the enemy, be that memory and processing, or units on the map