1. For Yacon pix, no I don't have any. My crop failed in the rain so I'm waiting for it to clear up before I plant again. This was the situation all across the country this season, so it's not even at market. However,
a GIS turns up these. The tubers superficially look like Yuca, and the plants look like stunted sunflowers.
2. You can go both ways. It's a bit longer from seed, not that that matters to us really, and you get fatter tubers through VP.
3. It absolutely grows tropical - there's no photoperiod to it. If you can grow sunflowers, you can grow Yacon.
4. I don't see why not. Again, no photoperiod, and the amount of water you get naturally should make them very very happy. Personally, I'd try for the areas where you see
M. violascens growing (ie midlands, very wet areas, partial shade.) You'll have to monitor your plants, of course. They get grumpy about 35 C and above.
I grew them successfully in the Southern Ecuadorean desert with the proviso that I'd go and put ice cubes around the base of the stem on days where it got really hot (45-50 C in the sunshine was pretty common). They were in the shade of my nanners, which I think is what allowed them to grow at all. The heat stunted the plants a bit, but I still got golf-ball sized fruits off of them.