Answer to question 1: There is an inactive issue on this. Interested readers can look at https://github.com/deeplearning4j/deeplearning4j/issues/1737 to know the current update. However, the discussion loop is not very active.
Answer to question 2: As far as I know, there is no CapsNet implementation in DL4J. Also, I didn't see any open discussion/issues on this topic. I asked in the DL4j Gitter channel but nobody replied.
Answer to question 3: Both unsupervised pre-training and supervised fine-tuning can be performed using DBN. That means this probabilistic network is an intelligent choice if we do not have enough labeled data but still want to perform NN-based training.
Answer to question 4: Yes, there is an example ...