Once Adam and Eve sinned, they became imperfect as you said, so imperfect offspring were inevitable. Sin effected every corner of the creation, it put everything in a state of corruption. Adam and Eve were told by God to populate the world before the fall, hope this answers your questions.
God loves those who believe and those who do not and the same goes for me, you have no choice in this matter. That puts the matter of total free will to rest.
