1. The Loyalists I don't know a great deal about, but I do know they are supposedly incredibly powerful at culture warfare, they can automatically spread culture from their planets with no temples, and get even more buffs to their ships when they fight in their own culture.
The Rebels are similar to an undead or necromancy type faction, they have tech that can cause any ships they lose to come back to life (10% chance), or gain a temporary clone of an enemy ship they just destroyed (again, 10% chance), they also gain buffs when all enemy ships are cleared from a well, or after they've bombed a planet. Basically they're all about death and rebirth/renewal.
2. Somewhat covered above, worth noting as well is that the Advent Rebels can gain shield restoration for their repair and antimatter platforms.
3. Swarm and debuff. Each type of Corvette has their own debuff they can apply on attack, and they stack with repeated activations.
TEC Loyalist = Slows Phase Jump Speed.
TEC Rebel = Reduces passive regeneration.
Advent Loyalist = Reduces %age chance to hit.
Advent Rebel = Increases energy weapon cooldown and antimatter recharge times.
4. Can you say increased phase missile block in culture? Also the Corvettes and new Battleship are excellent additions to the Advent fleet.
5. Well let me put it this way:
Advent Loyalists = Join us or die.
Advent Loyalists = Cleanse the corruption.
The Coronata assimilates the nonbelievers.
The Eradica purges the impure.
(The Eradica also has the whole death and renewal thing going with it's first and third abilities.)