Jenna,
There is a little tab on the end of the little bar the lever moves when you open it that rests against the bobbin.
If the lever isn't opened the tab does not touch the bobbin and it will fall out. I just tilt the bobbin case with the face up so the bobbin doesn't fall out when I adjust them.
The little peg is on the bobbin winder. It engages the notch on the inner edge of the bobbins shaft to spin it. They can wear or get broken.
Joe