Speaking of Mel, can my opponent play Abandon on my spell while I control an empowered Mel, Newly Awakened? What happens?

They can play Abandon targeting your spell. On resolution, they will Predict, but nothing else will happen.

Mel, Newly Awakened says “your spells and abilities can’t be countered.” If the spell can’t be countered, Abandon will attempt to counter it and fail, and then it will replace the event of it being put in the Trash with it being returned to its owner’s hand. However, that event never occurred, so there is nothing for the replacement effect to replace. Thus, Abandon will resolve to no effect. The replacement effect only functions within the limit of the resolution of the ability (it’s not a delayed replacement effect that specifies a duration), so even if the spell resolves later, it will go to the Trash as normal.