I doesn't appear in your pics that there is much distance from the peak of the shed roof down to the top of the door. This might not be much area for support depending on how high your mast is going to be. If you use a long mast you might be able to just bolt it along the side like this. Common lag bolts, washers, and a steel strap (or 'clips' as Mackbig suggested above). Build out the bottom from the shed with a block of wood and bolt to that.
Chain link fence top rail makes a good mast pole.