Couple of questions about battles.

[Myth]

1. Trebuchets. If I remember correctly you cannot move them so they cannot be used to break the inner castle walls, right (I hope the design flaw where you can scale the inner walls once you climb the outer walls is fixed)? Is it possible to fire the trebuchets from inside the walls in defense battles? Are they useful in the field battles?

- You can move them in M2TW. You're thinking of Stronghold and Stronghold: Crusader, where they are immobile
- In vanilla M2TW they have plenty of power to tear down several walls. In the Stainless Steel mod even a pair would be hard pressed to knock down a thick section of outer wall.
- Not sure about that, do you mean you can walk along the crenelated paths and go into the inner courtyard? If so, i've never done it as it seems a pretty bad way to design a citadel. It's impossible in Stainless Steel.
- Yes, though with dubious effect
- No, in field battles Mangonels and some gunpowder artillery do a much better job.

2. I understood the command stars give morale. Is that means the +/-morale traits are stackable with the command stars? Also in the battle are the chivalry points actually equal to the command stars?

Command stars give morale. Chivalry also gives an extra morale boost. Both stack with +morale traits. This is useful when leading non-professional troops or when fighting things like the Mongols and Timurids

3. The swordsmith guild gives tiny swords at the units which are trained/retrained there. What kind of bonus is exactly this? Is it worth to transport the units for retrain to give them those swords?

As Nelson said, they give +1 attack, but that's actually a pretty significant increase. They really imbalance autoresolve for some reason.