1) Ok.. For one Doors of Death (DoD) are 100% in Greece or Rome... Coz last line of Prophecy always gets fulfilled at the end.. So that's where DoD are.. Foes bear arms at DoD.. Means Romans and Greeks unite to close the doors.
2) Fire or Storm - Fire is Leo for sure - No doubt what-so-ever..
Storm is Percy or Jason or both.. But now I am thinking it can even be Khione.
3) Frank will die in the end for sure..
4) Hazel will marry Leo at age of 20 as shown by the Judges of Underworld. She will live her full life this time. And even Pluto had told her that her curse will be washed away by descendant of Neptune which I am sure is Frank. Pluto also had told her that she was born too early, So this time she will have her full life and marry Leo. Gaea had also told her that she'd marry Sammy so this time it'll be Leo. (I don't know whether Sammy is Leo's grandfather or Leo's 2nd or maybe 3rd rebirth)
The line says "To storm or fire the world must fall." So I am guessing that the world is Gaea and she must fall.. (As per reviews I received)
