Welcome to the board!
Here are a couple of thoughts:
1 - that’s exactly what you want with the wood, but at times you will get some ash.
2. My firebox is off just a bit, not much. It shouldn’t compromise your cooks as is. I didn’t really notice it much in your picture.
3. The firebox lid not closing? I see the wood is in the middle of the box, but sometimes the chunks will keep it from completely closing. When you take it out of the box and no wood, does it close? Wondering if there is something on the back of the smoker that could be hanging up on the overhang?
But otherwise, you are on your way to lazy q! You have the start of a good seasoning inside the box!
Hope that helps!