If you are talking about aquatic snails, they will die shortly after adding the moss to your tank, as long as the moss isn’t in a water feature. I wouldn’t mind the snails but that’s just me.
When adding it to your tank, it is best to keep it really moist for the first week or so. This way it can transition from aquatic to terrestrial. Java moss needs relatively bright light and grows very well and very fast under CF.
I wouldn’t cut it into little pieces. It spreads faster as a clump because there are more ends for the moss to spread from. It can be propagated from small clumps better than individual strands…but be sure to tear the pieces from the original clump instead of cutting it, that way you get the entire strand.
Java moss, like all moss has a “root” end and I guess you could call the other end the tip. The “roots” would be holding the moss to the substrate while the tips photosynthesize. But if you mean that your java moss is growing in one direction as a clump, like to the left or to the right, than that is probably because it is growing towards more favorable conditions, brighter light or more moisture.