"Η Ελένη έχει τη Βίβλος", I think. Despite the -ος ending "Bible" is feminine and the tonos shifts back, which helps to differentiate it from "book". I think if it's written it should also be treated as a proper noun and capped.
Yes, and thumbs up to all you have written Sean. That's exactly as it should be.
"Η Βίβλος" = The Bible "Το βιβλίο" = The book
So it is "Η Ελένη έχει τη Βίβλο"
έχει means he has, she has, it has.
It does not have a gender "masculine, feminine or neuter. Only nouns have genders.
Tips notes in Basic 1 and Basic 2 have good explanations. TheTips notes are on the homepage right under the list of lessons. You should make it a habit to refer to them.
Here are some other references https://www.duolingo.com/comment/22040507