I'm impressed! You got further on this riddle than I did when I read the book. The title of the book will be revealed at the end of the quiz. I couldn't understand the meaning of the verse, so this is well done.
The answer to Bilbo's question is put in spoilers:
-Homer's tale of Troy is the Illiad - correct
-But Iceland is not the country of the midnight sun
-Our Christ preyed in the Garden of Gethsemane - correct
-Good fortune comes from a four leaf clover, that is correct. But where does this belief come from? Where does the four leaf clover grow
-North is indeed the missing one here
-One of them is correct, but I think only one of them can be correctly discribed as "vanquished here"
-And yes, Eve is the mother of all sin - correct. Apparently, Adam was innocent as a lamb