Welcome to the forum and our community here! We, my husband and I, have just recently went through the whole process of applying and getting D7, so our experience is still fresh. Even though we used services of Ei, I still can answer some of your questions.
1. no, you can skip a fax #
2. yes, you can skip it, if you are not invited by a company.
3. I have posted some other answers and tips regarding the application which you should be able to find here:
also, try searching just “D7” and you should see more posts and discussions.
Overall, we found a whole visa process to be easy and smooth. And surprisingly very fast! We, those on the West coast, are assigned to a San Francisco consulate and have to go via VFS, which requires you to apply in person. For those on the East coast, and assigned to a Washington DC embassy, everything could be done by mailing to VFS.
I hope it helps. good luck!