How to line / fill the ugly gap around my newly hung shed door
Part of the "ugly" aspect of your door is that the gap is not uniform. The bottom hinge gap appears much smaller than the top. Correcting that by adding shims to the bottom or re-positioning either or both hinges to accomplish even spacing on that edge. 

One can hope that in so doing, the gaps elsewhere will even out. That alone should improve the appearance, perhaps not requiring gap seals.

If the internal door stop refers to a need to prevent the door from turning inward too far, a wooden strip across the door frame, inside the building, hanging down only far enough to contact the closing door will provide an internal door stop of sorts.