How does transplanting different sets of Sharingan eyes work?
After quite some searching I came to the sad conclusion there is barely any information available on how the 2 eyes get fused. Then again we can make some educated guesses thanks to some of the shown footage in the anime.

In episode 136 Itachi shows Sasuke how Madara got his Eternal Mangekyou Sharingan (EMS). Showing the following picture 



With this image we can deduce that the old eyes are not removed from the body, meaning there are 2 pairs of eyes in the body from that moment on. The most plausible reason to pass would be that the 2 eyes fuse in a similar way as to an artificial limb getting attached to a body. This would also explain the reason for blood ties as your body might reject people who are not directly blood linked.

This would also answer your first point, as the eyes fuse it does not matter whether the begin point was the blind eye or the still functioning eye as they will become one after all

How do the eyes exactly fuse? and how do they put 2 pairs of eyes in a body to begin with? Guess this is a sort of anime magic which is not really uncommon in Naruto to begin with (small sample (careful contains spoilers if not up to date with manga)