If you play long enough you'll eventually get to know them all, but anyways on to your main question...

The issue here is that you're playing on "unlocked teams" settings.  The AIs tend to make alliances amongst each other early and often, but expect you to complete missions for the right to be considered for such a privilege.  As a result, especially in multi-system scenarios, this can turn into everyone against the player.  The easiest way to prevent this is to turn on locked teams, which will prevent the AI's from allying with each other and will make them treat you the same as anyone else. 

If you get a lucky break, one or more AIs may end their mutual alliance and turn against each other, usually because it has no more enemies (AIs almost always shuffle alliances so that they have at least one enemy if any other players are left). I saw it happen after I killed an Advent AI: the other Advent and a TEC AI ended their mutual alliances and turned on each other (and witnessed the Advent AI suffer an overwhelming defeat - lost 6 capital ships, three of them level 10).

also, trade agreements only give trade bonuses. what you really need for a true alliance is a ceasefire (60-70% allegiance) or a peace treaty (80-90% allegiance). those numbers are rough estimates, but close enough that you get the point.

I believe <85% is the point where they break Peace Treaties.

If you only have a Cease Fire, they'll stay with you until you drop below 40% or around that percentage.