3. How to get character trait? (+1 strength, stamina, etc), are trigger from random events?
4. Is it possible to laid merchant (beside the farmer)
5. When you train your girl in farm, is there any difference between train by human/animal/machine?
I don't know about the first two questions but I can answer others.
3. Those come from leveling up your character. Your character's exp is "Prestige" which you get from banging chicks or having your girls work as whores. The higher rank the girl, the more prestige. When you level up, you should also be able to put a point in any stat of your choice. (Strength, Int, Charisma, Speed).
The specific upgrades you get are dependent on what class you chose at the start (either warrior, mage, or rogue). You'll also unlock more unique traits related to the class, like the mage's spells or the rogue's love gain increases.
4. Without spoilers, you can have events with the main shopkeeper and the stallion woman. I think it's just those girls who get stuff but I might be wrong.
5. Girl's have a specific weakness to one of the 4 types of creatures in the farm (stallion, beast, monster, machine). If you train her with her weakness, I
believe she trains faster but generates more fear. She
might also be less willing to do the training.
Your farm creatures can also level up, so higher level ones will do the job better. I don't really know how significant them levelling up is, I just stick with weakness when I can.