Whilst I understood the reason for the splitting in the characters memories I didn't really buy why the splitting would have been rectified when they both were reunited. Is it just the simple fact that their memory of each other on that previous time line was confirmed?

As for whether or not it was the same Jake... the fact of the paradox suggests it was. However ....

later books spoilers...

Spoiler:
Wolves of the Calla suggests that they are seperate Jakes.


That being said, it could be explained to some extent by the whole quantum universe theory where seperate universes are spawned considering what decision is made. Therefore the two Jakes are now seperate, one alive, one dead, but before Roland saved Jake by killing Mort they were the same. Of course I'm not sure why the save Jake would have the memories of the other (regardless of whether or not they are the same, since he was saved before he met Roland) but that could be put down to Ka-tet and his power in the touch coming into play.