Right, well your camera issue is a fairly easy fix. You may have noticed (and this would go in a proper bug report) the following behaviour when trying to work out what was wrong:
- There is definitely a Main Camera in the Level_01 scene Hierarchy, and the Inspector shows that it is active
- Playing the game starting from Level_01 the camera works as expected
- Playing the game starting from Start the camera does not work in Level_01 and disappears from the scene Hierarchy during play
So your issue is that something is deleting your camera at runtime for some reason - specifically when moving from Start to Level_01. As to what… Well the only thing we’ve done in this project that deletes anything is the MusicPlayer script, and it turns out you have one attached to your Main Camera.
Essentially, when you switch from Start, with your music playing away, the script on Level_01’s Main Camera activates, detects that it’s duplicating the Music Player effect (which has been carried over by DontDestoyOnLoad) and Destroys the gameObject it’s attached to - your camera.
The solution is simple: just remove the extra MusicPlayer script from the camera - you’re not going to need it there for any final build, since the player should always be coming from the Start menu and so bringing the MusicPlayer from there. If you really want a MusicPlayer in Level_01 (e.g. to ease the tedium of testing), then create an Empty GameObject in the hierarchy and just attach the script to that - then both can be safely deleted when they’re no longer needed.
Exactly the same issue is behind your Game Over button problem - you have two extra copies of the MusicPlayer script on your level manager, so even if you start on Level_01, at least one of them has to be a duplicate - destroying the object and meaning your button can’t access the level manager script. Same solution - delete the rogue MusicPlayer scripts and everything works as it should. 
Hope this helps, and good luck with the rest of the course!