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As Alex said, the enhancements get discarded. If Death of Firstborn is played and only one evil character is in battle, your opponent must present a new evil character before he can play Grapes, since no EC would be in battle, and Grapes isn't an interrupt.
Your opponent is allowed to play a dominant before Battle Resolution, as long an evil card was in battle after the first evil character was removed with Death of Firstborn.The last line is clarifying text and is not relevant. Normal Battle resolution occurs if no EC is brought in and no dominants are played.