Stackers game logic?

I'm trying to get the Stackers game logic down as practice to further my coding knowledge. Most of you guys are probably familiar with the arcade game, "Stackers".

In my current stackers game project, I made the movement natural instead of tile-based.

The problem I need to solve now is that, when the player taps to stop a block from moving and he doesn't get a perfect align with the previous block, how do I get the difference of the previous and current block so that I can spawn the succeeding block to be smaller in width, taking into account the difference?

In addition to that, I also want to show the segment that is off the ledge to fall down. How do I do this when my block is just one sprite(how do I slice the sprite, if that's even the correct way)?

If anyone can provide some snippet of code or pseudo-code for the logic, I'd greatly appreciate it.

Thanks