Could you expand on this? Not too familiar with Killzone.
WW3 happens and the various nations and coroporations still standing band togeather to send out colonization fleets. A number of these are lost (some in suspicious circumstances) with no further contact recieved in some cases but some succeed. 1 of the lost ones could easily be the 12 colonies
Approx 256 years later the events of KZ1,2 & 3 take place where the only 2 habitable planets in the Alpha Centauri system go to war for various reasons.
Looking at the wider verse Earth has the only proper fleet. They take a very much hands off approach to their colonies. As long as they provide the materials Earth needs to survive they pretty much self govern. Earth is never really expanded on much but its supposed to be way above everyone else in tech and military power.
All the other colonies (Vekta being the richest) having only orbital defense stations if they can afford to build them. Helghans fleet in KZ1 was repurposed colony ships and in the further games the new ships ( around 250-300 metres) are primarily for transport (troops, tanks etc )and close air& ortilary fire support. From KZ2 on Vekta's ships (built only for the counter invasion in KZ2 and around 700+ metres long) ) were impressive in that they built so many in 1 year but even in verse were acknowledged as knocked togeather. They like the Helghan ships of KZ2 are troop transports and fire support ships but they do massively out range Helghan ships due to their Snow missles.
Theres no widespread use of fighters in space combat (mostly because thirs no need I presume) The only space fighters we see also double as you guessed it transports. I think they hold about 10 troops IIRC.
Weapons wise they use mostly conventional firearms and missles etc with some exceptions. The Vektan cruiser main engine doubles as a massive nuclear laser, the Helghast stole a Vektan neutron bomb, and spec ops especially in the later games have accesss to variable power rail guns. Whilst the Helghast have Petrusite (crazy space magic mineral native to their planet). The .ore exotic weapons are fitted to ships and massive mechs mainly.
Defence wise cloaks are standatd on snipers and high end troops. Ships can have shields and energy absorbant armour.
FTL (warp jump) is around 108 ly per hour and they have real time comms accross the system.