1. Isn't an issue. They make inference on a sample by sample basis. The network has no memory so it won't expect a 50/50 distribution on the test set just because its trained like that. Having a balanced distribution is the exact right thing to do because you do not want the network to be biased to one or the other class for any given sample. If it were unbalanced the network could achieve almost 0 training error by just predicting negative all the time. This is not what you want.