The one from the Rat goes away after you take a certain amount of steps. However, Lycanthropy is pretty damn rare, though it is permanent until removed with a Remedy. The Goblin Merchant sells the Remedy sometimes. There is also a Remedy in the little wooden crate next to the tent when you first arrive in the forest. Lycanthropy can be useful for physical combat builds as it does increase your Strength by 50% and your Vitality and Agility by 20%, but in your case it might be better to buy the Remedy when it is available from the merchant. In the future this state will actually turn you into a Werewolf if not treated in time (a male Werewolf that is).
You only need the Construction Skill to fix the Bridge. While for Lockpicking you need the Guile Skill.
You can also use Climb Lvl 2 to climb up the vines at the Brothel exterior and go through the second floor window instead of unlocking the door!