I never worry about fighting a faction really, but NwabudikeMorgan opens up a good point: be friends with factions you are nearby by having relative values and hate factions which are far away. In one of my game as the drones, Yang declared war on me and they were away and didn't do a thing.
My point to dealing with threats is this: Give factions tech that doesn't contain new weapons or armour, if you do, you'd kick yourself once you attack the faction, because their new weapons and armour will help defeat you. You need to research each faction with the handy AC booklet (strangely I have 2, since I bought AC original then AC with crossfire): if Morganites give you threats don't be threatened! They're a weak faction in military, due to support, Free Market and if they choose wealth, typically they're peacemongers. If Gaians threaten you, just boost your soldiers' morale and get Neural Amplifer, so if they attack, you should have a good chance of winning and quit using Free Market otherwise your attack against natives is weakened by 30%. If Spartans, Hive, Peacekeepers or Believers threaten you, if they demand about 200 credits, then give it to them, if its higher than about 800 or has a high percentage of your remaining money, refuse, if they want tech containing weapons, refuse, and fight. if University threaten you, they're weak too, if you use probe teams and natives--refuse and fight.
For other factions in crossfire: if drones threaten you, they're fairly tough since their production is very good, fight them if you are ready (in fact that goes to all factions).
I never give factions my tech or money: it's either trade or forget it.
We're actually supposed to be talking about Fusion Planet Busters anyway, so, to know if they are building one:
Infiltrate datalinks
Get Empath Guild (recommended)
Be governor (if my recommended fails)
Empath guild and being governor place an infiltraitor in every base and faction. Use probe teams to cause severe blow on PB production or attack the base, and they'll eventually change production.