The dojo that I trained at when I learned hard falls had a similar approach, we rarely worked on it and were just sort of supposed to figure it out when the time came. To answer your questions in order,
1. I think that Bookman Sensei's video on ukemi presents a nice way to learn to breakfall, and it isn't all that expensive. Or you can learn by watching, with the occasional "your feet are wrong" comment from your sensei or sempai (this is what I did).
2. I don't think that there really is an appropriate kyu rank where people become comfortable with breakfalls. Proficiency, in my opinion, would be when you can comfortably breakfall from anything that may require it, including a badly done shiho-nage. I would think this would take years.
3 and 4. If breakfalls cause pain or injury for any reason, don't do them. Especially in your case where you have a previous spinal injuries. I know a lot of upper dan ranks who do not breakfall for various reasons. I can't speak for your dojo, but I would be surprised if you were held back from testing because you could not breakfall for medical reasons. One thing of note though is that you should communicate this clearly with any uke that you train with. Once you have achieved shodan rank, or even upper kyu rank, many will just assume that you breakfall without bothering to ask you.
There are really very few techniques that absolutely require breakfalls. Play around (with an uke that you trust) with variations on falls, finding those that are the most comfortable for you. I think that ukemi is very personal, and varies considerably from person to person.
Of course, these are my opinions, not facts, so take them for what they are worth.
Happy and healthy training,
P.S. After posting this I saw that Jun sent a reply while I was writing that says about the same thing. Sorry about the redundancy!
[Edited by Shipley on July 25, 2000 at 04:03pm]