Yeah, the equips are broken sadly.
As to how to leave the town, you need to head into the 2 story building with a golden sign and after that cutscene, you cross the ledge to the left of your cabin. From there, if you try to leave the map, the game progresses in a fairly obvious manner.
If you are still lost after that, you need to talk to the mayor, after you've grabbed the chest to the left of your cabin (the one that is past the ledge)