How do I ensure I have split my tables without loss of data?
A classical theorem in normalization theory says that you have a lossless join (that is a decomposition of a relation such that when you perform the natural join of the decomposed relations you obtain the original relation) in the case of two relations  if and only if the intersection of the attributes of the relations contains a candidate key for one of the two relations.
This result can be generalized to a decomposition with any number of relations.