for the "i want to offer you my sword" follow the "i wish to ask you something" its hidden in there.
as for the merc contract, its a proper ball ache, just ride around trying to imporve your rep with that fration, and improve your rep a bit, killing bandits and helping out patrols/foragers is a good way. and asking mayors for a job, if it involves killing is also helpful, and of course help out your choosen frations lords when they fighting.
but dont hold your breath i had to follow the swedes for over 150days before the merc contract came up, i was very tempted to just **** em and go somewhere else but i held on and it popped up. i think in the end the king offered me the merc contract, so just keep mugging him asking about "special missions". or ask lords who you have a decent rep with, 15+ yields better results, so 4 letters per lord