Three of the disciples, Peter, James, and John, had been with Christ on the mountain, where Christ was transfigured before them. This left nine of the disciples elsewhere, and now Christ and the three that were with him re-join the other nine.
The child was demon possessed. We need to bear in mind that the New Testament does not use the term demon possession as a kind of ignorant explanation of other illnesses. Demon possession in the New Testament is very exactly described and is quite distinct from other conditions. You may be demon possessed, and also at the same time have other illnesses and impediments and diseases, but these things are not confused with each other. In fact, the demon possession may have given rise to the other things in those cases. But demon possession is a specialised distinctive and quite precisely described condition in the New Testament. There would appear to have been quite a lot of demon possession, and an increase of it, in the world of those days prior to the coming of Christ. We are talking here about involuntary demon possession: people becoming demon possessed who do not seem to have invited this condition, who had not been meddling with the powers of darkness and extreme occultism. One of the great benefits, according to the New Testament, of the coming of Christ is that he ended involuntary demon possession for all, so there was no more after Christ. He said he had come to cast out the demons. You only have demon possession today if somebody is knee-deep in dark arts and occult practices, and spiritism. It is possible for a person to put themselves into a condition where they can be subject to demonic activity, but here it was clearly involuntary, and naturally the father of the boy is deeply distressed.