After completing Dawnguard, I still have a few questions.

So, Vyrthur made the prophecy? Does this mean he has written the elder scrolls?!

Also, the quest-line makes you collect 3 elder scrolls, while at the moth cave you only have to read/can read 1 of them.

So the other 2 were not needed, correct?

Watch the cut-scene again. You will see that after you open the first scroll, your character will then open the two other scrolls as well. This is not under your control, it is part of a cut-scene.