The Spyder, being a reverse trike will handle a hard turn. The typical conversions are a triangle footprint with no stance up front to counter a roll. Weren't the Honda Big Red trikes banned due to spinal injuries?
Yes, although I believe it was an "agreement" to stop selling them as opposed to an actual ban.
For the H-D and Gold Wing trikes, I'm not sure where the lawyers are. I'm not sure a company that builds motorcycles wants to get lawyers involved given that their normal product falls over every time when it stops unless the rider stops it happening. But, a motorcycle has predictable steering characteristics. With a trike, the rider's steering input has to switch phase when the inside wheel lifts off the ground. With three wheels on the ground, turning the handlebar right turns the vehicle right ("car" steering) then when the inside wheel lifts off, the rider has to turn the handlebar left in order to bring it back down (countersteering as a motorcycle does - it is now acting as a two-wheeler). That doesn't sound very intuitive. The Can-Am Spyder is low enough to the ground that the center of gravity is low enough that this doesn't happen easily (and stability control intervenes and says "nope" by slamming on front brakes).
While I was at the Gap (actually, while we were at the overlook), there was a nasty crash involving a trike about halfway along. Can't find any news articles about it, so I won't discuss what was indirectly told to us later. In discussing this back at the resort, we chatted with someone who had been involved in someone else's trike crash about 6 months earlier. He had a backward-facing GoPro and showed us screenshots. First photo, trike had just passed by in the opposite direction and had the inside wheel perhaps 100mm above the ground. Next screenshot the trike was at about a 45-degree angle. Next one it was almost on its side, and this is about when the rider/trike (not sure which) had a glancing impact with the bike following behind the camera bike. What happened after was out of view, but the trike rolled over and went up the embankment, then came back down and bounced back onto the road, into the path of the
next bike in line, and that was a hard hit. Destroyed almost-new ZX10R, rider of that bike hurt his back. The trike rider was only wearing a beanie helmet and no other safety gear (go figure) and was also badly injured.
Yes, bad things can happen if you exceed the physical capabilities of ANY vehicle ... but single-front-wheel motorcycle-conversion trikes seem to have a very low performance envelope, and when exceeded, they seem to spit the riders off in front of them and then land upside down on top of them.