A lot of what you're mentioning needs work, I agree. I made the menus placeholder for now, next demo will have them properly working and explained. The "main level" isn't an actual level, it is just a sky, so don't worry you didn't miss much. Run toggle needs to be worked on, right now you walk if you hold the interact key. I plan to have an option toggle for toggling run/walk and setting which is the default (default walk OR default run). The camera control might change, I've been considering making it work less like Mega Man Legends and a bit more like modern 3D game cameras. Music stopping isn't intentional, I set the wrong pause behavior of the audio player it is playing from. Main menu is a bit buggy and lacking in design, I agree. It will be getting some big changes in the near future.
Thank you for checking out the demo and providing feedback. A lot of what you mentioned is already intended to be fixed/changed, it all definitely reaffirms those goals.