You are surely enthusiastic about this.

Let's have some constructive criticism.
Elven Bow
Immediate trouble. Elven bows mean Elves, and that breaks the no-fantasy Mount and Blade setting. Call it something else, like "Whistler".
This weapon becomes available at 30 STR and 10 Power Draw.
Rarely anybody gets to 30 Str and 10 PD, except cheaters. Lower to, say, 24 Str and 6 PD.
1. Quest giver tells you his favorite board game has been stolen by his jealous friend. He tells you he will reward you with his strongest weapon if you can retrieve his game. He says his friend left to a nearby town.
Board games were played by the aristocracy in medieval times, the peasants played with mud. What are the quest-giver and the thief? Rich merchants? Idle nobles? Genius villagers?
If you are introducing a board game, explain what it is. Chess is probably the easiest answer.
2. Going to the tavern of the nearby town and talking to the barkeep will get you the information that he tried to rob drunk patrons while clinging his board game tightly, and when he left the town was screaming you Orcs will never catch me. The bewildered barkeep tells you the village he was headed towards.
Ok, you may find it funny, but you are beginning to stretch credibility here. Unnecessarily, in my view. How likely is for a well-off person like the board-thief to pickpocket random people in a bloody tavern?? He may as well have offered free blowjobs, why stop with random theft of small change. Meh.
But let's go with kleptomania for now, as it provides motive for the original theft. Maybe make it more believable or hilarious - let's say he took a room in the tavern, but was then thrown out because he tried to steal the tavern-keeper's baby rattle toy (in keeping with his love of entertainment paraphernalia), or the town's bishop rosary or something else.
3. Talking to the village elder he tells you that he did see him after he was caught peeping on the young girls in the baths. When he was chased out of the village he was screaming something about Black Riders. The elder tells you the direction he went in.
Just no. Remember that making him a kleptomaniac is already taxing on the player belief and immersion. Making up more random stuff is not hilarous and the player will simply give up on the story at this point. If something needs to happen everywhere he went, use a logical pattern, like stealing games and toys. For example, he shoveled all the villagers' mud on a cart and took off.
4. Upon arriving at a nearby town you head to the jail guard who tells you that he is locked up inside, but he won't let you see him.
5. At this point you have a few options: Persuasion check level 4, or 300 gold.
That's ok. But why was he locked? Maybe he tried to unload and hide the villagers' mud in the town well.
6. After that the guard will let you talk to him, he says he was caught trying to steal a horse in town so he could get to his beloved who was apparently a Elf maiden. He tells you he wasn't able to buy a horse because a group of bandits mugged him for everything he had and he lost the game to them.
No no no. No Elves, please. Even if you have Elves, they'll likely avoid humans, and only the top human guys can date the Elven chicks, not random thieves.
The bandits mugging him is somewhat contrived and reeks of "kill bandits quest" cliche - there are enough of those already. Why not make a town militia group that stole his stuff when they arrested them? And you can ambush the guy who stole the board at night when he's on patrol duty in the town. He can have some friends with him.
7. Nearby bandit group spawns (Small group(5-10) but fast moving 6.0) once they are defeated you retrieve the board as an item.
Yeah, town scene battles are more fun and challenging, especially if you must fight by yourself. The player's party is already more powerful than any bandits at this point (late mid-game).
8. Returning the board to the quest giver grants you the Elven Bow.
Maybe he describes to you a hiding place in some village or lair location, where you find it in a chest?
The story is still very weak. Why would you get an extremely powerful and expensive weapon for a board game?
The tasks are not related to archery at all, but tracking a random kleptomaniac. Needs at least one archery-related task, like taking a difficult shot.
The tasks are not challenging enough. You go to a few places and fight a few guys. Meh. Now, surviving an ambush by 20 archers by yourself is challenging and awesome.
Everything worth doing is worth doing well. If you give someone a fish, he shouldn't slap you with it. Typing is hard if the laptop is in the other village. Random didactic nonsense.
