The question is never what forces the ball OUT of the EZ, but always what forces it IN, that is, over the GL. So the question to ask is not quite "how did the ball get there," but rather, "who forced the ball across the GL?"
So, in your first scenario, we'd need to know where R muffed the ball: if it was already in the EZ, then clearly the bad snap by K forced the ball into the EZ, and you'd have a safety. If R muffed the ball in the field of play, then the R would have to rule on whether R imparted a new force that put the ball in the EZ. If so, then it's a TB when the ball becomes dead there; if not, then, again, it's a safety.
You might review 8-5-2 and 3 regarding safeties and touchbacks.
This is a pure judgment call by the R. Footballs bounce funny, so you just have to make your best judgment about which team forced the ball across the GL.
You asked about the TB: barring a penalty, it's always 1/10 after a touchback. The team is awarded a new series per 5-1-1.
Last question: a blocked punt is still a kick, and so if a kick goes into K's own EZ, K is responsible for forcing it in.