Hey there, thanks for checking it out!
1. Basically yes things are reskinned for flavor the damage is based on the size of the item.
2. Correct again! Using magic in combat requires a magical weapon and does not deal damage on its own, the idea is that magic must use a conduit (weapon) to hurt another living thing.
3. These adventure moves are meant to be used to track the time you spend while adventureing and are intended to be used every time to help keep track of the time of the day, and travel distance. But you can feel free to hand-wave stuff if you'd prefer. I use them as written because I'm a fan of hex-crawling mechanics such as these moves.
4. Stepping up your dice is just increasing it to the next # sided die. For example, if you have a magical wand (d4) and you Become Stronger you can "step it up" to a d6. As for Toughen Up you can't use it on heavy armor. However, I may have to change the wording on that to make it more clear, or maybe allow it to add to heavy armor as well... I'm not sure yet. But if you do use it on heavy armor and it works out well let me know!
Sorry for the late reply I hope this helps!