Gives us a few pieces of the puzzle. Aya was last seen the day of the Tanabata Festival, but Aya remembers it being the day before the festival when she ends up in the future. Erika supposedly had a conversation of some kind with Aya on the day of the Tanabata Festival, and may be the last person who saw her before she disappeared. But, Erika is also curious about what Aya did after leaving said conversation, so it's unlikely (but NOT disproven) Erika was directly involved.
Good catch. Given the Tanabata theme, it could be a wish Erika wrote and hung up on the bamboo. She must have been tormented with guilt ever since, in that case.
This reappeared Aya seems to be fully functional and capable of independent feeling and thinking, and also corporeal enough for a check up at hospital, so I think we can rule out the "ghost" and "Koto's and Erika's projection" theories.