Just regular vulcanized rubber will close itself up a bit for smaller punctures, but larger chunks or gashes are going to be messy. I believe you are thinking or runflats; tires with extremely thick sidewalls which are enough to hold the tire up for a while even after a major puncture.
As for your suspension, mixed with the morphability of your tire, it just won't work, even if it is triangles. just think, if your wheel hits a bump bigger than an inch or so, it will get forced inwards on itself, like a pneumatic tire does, except with that lower shock where it is, the the portion of your tire being turned inwards is going to at the very least push sideways on the shock, providing extreme stress, which will quickly result in your shock wearing itself out. At the very most, the wheel will simply snap it off.
Now, if those shocks spin with the wheel, they are simply too far apart to really be effective, at all. you are going to have the wheel transferring between times of no support at all, to suddenly having a lot of support at a single point, which means you will have a very rough ride, coupled with three spots which will wear away very quickly.
I don't think you're trying to have Regenerative braking; what you're saying is that you're simply lessening the amount of energy going to the wheels in order to brake? that's something entirely different from regenerative braking. The reason a Prius gets such good mileage in the City is because you are constantly braking, and the car harvests some of the heat energy created by the friction of your braking. So, your braking system might work, but regenerative braking is the incorrect term.