Welcome to the forums, and I'm glad you're enjoying the game!
In terms of the Acutians attacking the Skylaxians, it might be just pirates or skirmishers -- probably one or the other. Why exactly you can't intervene is something I'm not sure about. The logic there is pretty complex, and we may have missed an edge case. A savegame where that is the case would be helpful to me next week after I get back in town, if you don't mind uploading one to mantis (see my sig).
In terms of the Andors showing up in that battle as enemies, in that particular case it's because they came to help the Acutians, who are their friends (presumably). They were passing by and decided to help out, and that overrides any sort of alliances in the immediate battle. You can set your own ship to not attack the Andors, though, if you wish. And then after the Acutians are trounced, just leave. If the Andors and the Evucks are BOTH in the federation, though, that shouldn't be possible. It doesn't sound like that's the case, though.
What version of the game are you on, by the way? Just to make sure you're on the latest version, because your first question was something where some past versions fixed some edge case bugs in that area already.
Regarding a battle with 4 races present, or any battle really, you can't control how other races feel about you. You see over there on the left whether or not they are neutral, hostile, or friendly to you. If hostile they will fire on you, otherwise not. But next to their icons there are little orange or blue icons that you can toggle for yourself that makes you either guns-free against them, or hold-fire against them. You can use that to make it so that you attack someone who is ostensibly neutral or your ally (which in turn, when they notice, makes them turn enemy against you in that battle). Or you can use that to hold fire against someone you don't want to piss off further by destroying their ships in battle. They'll still fire at you, but your shots will just pass through their ships without harming them. You can easily toggle these back and forth for any of the races at any time.