Why the "Split" feature is not splitting the body in two parts?

It's because the sketch referenced for the split ends mid-body. It needs to fully cross the body in order for it to work.

I think I found the main problem with the shell failures. There are some tiny surfaces along some of the split edges, see "problem area" pics attached.

I was able to get the shells to work by performing "delete face" command on these tiny surfaces prior to creating the shells.

The tiny surfaces are artifacts of the modeling approach, and could likely be eliminated by taking a different approach to the modeling.

Since the mouse is symmetrical, I also cut away half the part first, and then mirrored the bodies after achieving success with the shells. Most of the time it's better to build half the model and mirror it at the end in cases like this. I see you did mirror the surfaces, I think you just mirrored too soon in the process...

In general, the model is a bit messy, the surfaces are a little wrinkled and would probably be easier with a different approach but I'd have to work with it longer before deciding on the 'best' approach for this part. I think you've done well though, it's a very challenging part!