If I control an empowered blue mel, can my opponent rebuttal a spell of mine?

Yes — your opponent can Rebuttal your spell even with an Empowered Mel, Newly Awakened on your side.

Mel's protection ("Your spells and abilities can't be countered") only stops the counter part of Rebuttal — it doesn't make your spell unchoosable, and Rebuttal's targeting only checks Energy cost (≤[4]). So Rebuttal is legal.

The key is what happens on resolution: Rebuttal's controller chooses whether to pay [A]. If they pay, they take control of your spell and may make new choices for it — that's a control change, not a counter, so Mel does nothing to stop it. If they decline to pay, the "counter it" instruction is simply ignored ("can't beats can," Rule 54) and your spell resolves normally.

So Empowered Mel saves you from the fallback counter, but not from having the spell stolen.