Question

For the moon never beams, without bringing me dreams

Answer 1

B. The narrator admits that he grieves by her grave every night.

The narrator says that every night the moon shines and the stars rise (which means every single night) he thinks about Annabel Lee. Then, he states "I lie down by the side / of my darling ".  This shows that every night he lies beside her grave near the sea, proving that his love to her is never ending.