Yes, that is the Woodruff key, at the tip of the blue arrow. If you got it out easily, you were fairly lucky - sometimes it is difficult to get them out.
So long as the two points on the crankcase cover (sump) where you tap are directly opposite each other, it is not important where they are. I select them according to where the cover extends well beyond the crankcase itself, so I have room for the rubber hammer. Remember, just one light tap, then go to the other side, so the cover comes off in tiny increments without tilting relative to the crankcase. If it tilts, the holes the dowels are in will become deformed. Do not put a screwdriver or anything else between the crankcase and the cover, or you will damage the surfaces and cause an oil leak.
The clutch spring, which is of a type called a Belleville washer, is there to push the two halves of the dog clutch apart until the central spline disengages. You should be able to see marks where the tabs have been sliding around one half of the clutch, and marks where its outermost region has been pressing against the other clutch-half. I can't see it perfectly in the picture, but it looks as if I'm seeing rub marks under the tabs, and rust marks on the outer region of the other part. If that is correct, you have it in the right way up.
The tabs can't align with anything rotationally: whenever the clutch is disengaged, they are spinning relative to the clutch-half they are resting on in your picture.
