If you make it in 2 batches, they HAVE to be made at the same time. We've discussed this 200 recipe 2 batch thing elsewhere. It won't work to make them at different times, they won't fuse together properly. Although apparently Morbier used to be made out of 2 batches made hours apart.
LH is Lactobacillus Helveticus
Any strain of Lactobacillus will work. There will be slight nuances to the flavor of different bacteria, but they are all similar enough for an Emmentaler.
So you can use anything that contains L. Delbrueckii, L. Bulgaricus, L. Helveticus, etc.
An Emmetaler needs 3 bacteria to work,
Lactobacillus of some sort
As I think about the water issue, I come to the conclusion that it probably does not matter much when you are adding it, so long as it is the same temp as the milk/bruch. Adding water of a different temperature could trigger chemical changes, but adding water otherwise likely just dilutes the acid. Replacing whey actually removes acid, so has a more pronounced affect on pH. adding water is probably a little more gentle and subtle