Regarding the houses, there were different requirements depending on the city we looked at. For example, in Sadogashima the cost was about $20,000 for a house, but then the city would pay you $10,000 to $15,000 just to move there because their population is dwindeling, so the house would only end up being $5,000 to $10,000 dollars. The only requirement for the deal in Sadogashima was that you had to commit to live there for at least a year or two. Other areas we looked were between Tokyo and Sendai. The costs were about the same everywhere we looked, but some areas would only sell these abandoned homes to people with young children, or between childbearing ages, because they wanted their kids to settle in those towns as well.
I think the most unexpected thing was the zoning laws in some of the areas. For example, in a few cases, the house was in the middle of the block and the only way to access it was via a narrow alley between two other houses. Zoning laws allowed the existing house to be there, but prohibited it from being torn down and rebuilt, and some of them were in desperate need of being rebuilt. If you do decide to look at these free/cheap houses in Japan, make sure to do your due diligence so you don't get stuck with crap heap that you cannot do anything with.
We ended up buying an old condo just outside of Tokyo for about $100,000. It was cheap because it had been neglected and was in bad shape and somebody had died there. I put another $30,000 into it to gut and remodel it. It cost more, but I figured I'd have to get a Japanese drivers' license, buy a car, register it, and insure the car if I lived in a rural area, whereas I could get by with just a bicycle and the trains if I live around Tokyo. I opted for a higher immediate cost and a lower long-term cost by buying where I wouldn't need a car. There's a lot more to do around Tokyo as well. So far, I've been happy with the decicion.
I thoroughly enjoyed traveling around rural Japan for three weeks, talking to people and looking at houses. I'd do it again just for the experience.