hihi,
1. the main advancement mechanic is done during downtime with the various downtime activities. there is no traditional "leveling up" anymore, BUT that idea is returning in the next big expansion I'm working on, which will feature a few new mechanical options for folks.
2. so, you're right, it's intentionally vague for folks to fill in their own setting, BUT I do have a setting of my own that I based it off of. I released a few zines (Aberdeen 1 & 2) that detail small sections of my city, and i've been talking about my world building a bit on my blog, but there's nothing super concrete yet. Dungeon Girls also has some info about the city.
3. I believe you are looking at an older version of the PDF (it's been updated quite a bit). The new version says: "Whenever songbirds are in total darkness within a Dungeon, the GM rolls a d10 and records the number. Every conflict round or dungeon scene that passes, the GM ticks the number down. If the number reaches 0, the Open Maw enters the room. Turn order continues as normal, but at the end of every songbird’s turn, the Open Maw rolls on the table below."
4. They are more nebulous forces that can be called upon or followed. Though, they do get named in other sections of the book and future books. Like most things in the book, they are little hooks that might grab a player and drag them in a direction.