Any fertilized egg can potentially become a queen. When eggs hatched, the larvae are fed royal jelly for, I think, 3 days, after which they are fed pollen and honey. If a queen is needed in the hive, the workers will build several queen cells and the larvae in each cell is fed royal jelly the entire time.
When doing a split, always add a frame of eggs. If you put in just larva, the bees may have to choose to make a queen out of one that's been off royal jelly resulting in a poor quality queen.
A walk away split, from what I understand, is taking a hive with 2 deeps, simply splitting them into two hives, then walk away. One will have a queen and one won't. That problem with that method is if the box without the queen only has no eggs and older larvae, you may get a poorly developed queen.