Q1: assuming that we train the neural network with the same amount of training examples, how to set the optimal batch size and number of iterations? (where batch size * number of iterations = number of training examples shown to the neural network, with the same training example being potentially shown several times)

It has been observed in practice that when using a larger batch there is a significant degradation in the quality of the model, as measured by its ability to generalize. Large-batch methods tend to converge to sharp minimizers of the training and testing functions -- and that sharp minima lead to poorer generalization. In contrast, small-batch methods consistently converge to flat minimizers. Large-batch methods are almost invariably attracted to regions with sharp minima and that, unlike small batch methods, are unable to escape basins of these minimizers.

Neural Network Tuning