How far do 2 ant colonies of same heritage have to be in space (and generation) in order to fight?
Space and generation don't directly affect whether ants fight, that's all regulated with pheromones. Some ant species are more tolerant of different smells than others (see the argentine supercolonies mentioned above) while some species of ant have 'rival' nests that they are particularly aggressive to.

So I guess the answer is 'it depends'. On pheromones produced by the queen, and species. And probably diet/weather/local food availability/ some other things I haven't thought of.

I don't think it's possible for some ants of a colony to fight and others not to, but I don't have any evidence to back that up specifically.