As for running a pure military faction, sure, that's possible. Eg as mercenaries or bandits. You don't need to set up a big city, just a camp. As it has no intrinsic value, no one will bother you. Probably.
As for running a pure economical faction, that might be difficult... If you can't protect yourself, people will take your stuff, I guess.
As for bullying:
It will be very difficult to send huge armies far away. The more agressive your army policy is, the weaker your economy gets. If you send off your army to the other end of the map, where it will take them days to get there, you are hurting yourself more than the faction you are attacking. So warfare is location based, to some extent.
As for fairness, there will (maybe not initially) be kings that may have an interest in keeping peace within their kingdom. So it's their job to make sure the factions in his kingdom dont rip each others throat out.
But apart from that... we won't protect small factions. If you are a small faction, you better excel at something (fighting, a very high quality item/resource, etc) so you have some leverage. There is not only miliary power, there is also economical power and diplomacy. If you figured out a way to produce something so unique that everyone wants it, people will trade with you, and money buys power.
