1. This is the story from the Jewish Talmud, and the Book of Enoch, not from the bible. NOthing in the Bible is inconsistent. Granted it's speculation, but is speculation by people who were much closer to the events than we are today, and who spoke the language of the bible quite fluently, which we do not.
2. A possessed man still can make babies. The fallen angels did not make the babies, the men possessed by them did.
3. Josephus says they did, one in brick, one in stone. The Book of Jubilees says this record was copied by Cainan (he is the extra name in the geneology of Jesus in Luke, not in the matching passage in Genesis). I think, from linguistic comparison, he changed his name to Menes and founded Egypt. These records were collected and stored at Onu and are mentioned several times in Egyptian history.
4. Someone sent me a better link by pm when we were doing this last spring. A dozen html pages with pictures and detailed documentation. For now, this is the best I can find
GIANTS OF THE BIBLE
5. Immediately is a vague term here. They would not have possessed Noah's immediate family as his righteousness caused him to watch out for them; there is specific mention of this fact in the account of Cainan I mentioned. The technology was in active use until the tower of Babel confusion of languages. Goliath and brothers certainly was created after the Flood.
6. You are correct. The fallen angels did what Jesus said demons do. They wandered around earth looking for someone else to go into.
Please tell me what false doctrines would arise from following this to its conclusion.