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Very good questions. While I'm a pacifist, I know a lot about firearms, how they mechanically work, etc (likely an "on the spectrum" thing as a direct sibling has an autism diagnosis).

One of the important aspects of technique of firing a gun is the hold. Handguns are held differently from rifles and different types of handguns, sometimes even models of the same category, must also be held differently. This is both for marksmanship and for safety. For example, holding a revolver like one holds most pistols puts the support hand in front of the cylinder, which can cause burns or potentially digit amputations (I've heard of but have but haven't read any case studies of the later) due to hot gases and metal escaping from the gap between the cylinder and the barrel or holding many models of pistol too high on the backstrap is likely to cause the slide and/or hammer (if present) to "bite" the hand in the web between the thumb and forefinger. "Hammer bite" is painful but not usually a cause for great concern.

Bear with me (rawr) for a bit here because this stuff is relevant to your questions. Derringers, however, are notorious for a number of safety-related issues. First, they are small and seem unthreatening to those who are new to firearms. This is bad because they are also cheap and rather more prone to pose accidental dangers than other types of handgun.

Most basic Derringers are built cheap and simple. This means that, unlike modern revolvers, they rarely have mechanisms like a trigger safeties (mechanism that prevents the trigger from being pulled if a "sub-trigger" isn't also pulled), safety switch/catch ("normal" safety mechanism found on pistols, rifles, and shotguns that prevents the mechanism from firing until switched to "fire"), or transfer bar safety (a relatively new safety mechanism that reduces the likelihood of a hammer-fired gun going off if dropped). Do note that none of these mechanisms are infallible (see: Tiger King for a disturbing example of a transfer bar failing to function). Additionally, Derringers frequently do not have trigger guards. Their cheap and handy size leads many new owners to put Derringers directly in their pockets, without a pocket holster (a vital piece of safety equipment for ALL pocket carrying). With their lack of safety mechanisms, this has led to numerous and not infrequently fatal unintentional discharges (self-inflicted severing of femoral artery).

In addition to all of these, Derringers are frequently hard to hold correctly, due to their compact size. My thoughts on possible injuries from the .45-70 Derringer in particular are mainly related to the recoil. Because there is only the mass of the Derringer and curved handle to mitigate the recoil would be one getting full-on punched in the hand.

The force is exerted along the bore axis (if you do the physics vector chart thingies, the arrows point straight back down the barrel). The handle has a curve to encourage it to roll but that first impulse is likely going to hit on the tiny bit of the arc furthest back before it starts to pivot. Without extra padding in gloves or another way to deflect, dissipate, or distribute that energy, fractures to hand bones are well within the range of possibility. There are further dangers of holding the firearm incorrectly, like getting smacked in the face and/or dropping it, which could lead to accidental discharge.

Overall, this firearm is a fabulously terrible idea.