Is this sentence correct?
Whom should I marry among you three?
Among you three whom should I marry?
If I were ever in that unlikely situation, I should say, "Which of you three should I marry?'
When Bill said either, he meant that both are correct.
Your additional examples are all wrong.
They are all unnatural.
I's simply say:
Whose book should I carry?
Whose car should I repair?
Whose pen did I borrow?
If I am addressing three people, there is no need to mention the fact.