For the random numberes:
math.random(k) for a random number from 1 to k
Events:
TurnEnd, TurnBegin, PlayerTurnActivated, PlayerTurnDeactivated, UnitAddedToMap, UnitRemovedFrom Map, ImprovementAddedToMap, ImprovementRemovedFromMap, ResourceRemovedFrom Map
might be some more, but these are the...