1. First of all. Taiwan is not a UN recognized state so Taiwan does not have an EEZ. OK let us say Taiwan does have an EEZ. Taiwans EEZ overlaps with The Philippine EEZ. According to Internatinal rules, if two nation's EEZ overlaps, a delineation must be made by both sides.. if there is no delineation in place, any point at which the EEZs overlap will default to the nearest state. Now the incident happened 180 miles from Taiwan and 43 miles from the Philippines. Now do the math and answer the question; did the Taiwan boat intruded? An investigation in Taiwan has already confimed that the ship was outside the border of control of Taiwan.
2. The firing was done to disable the ship and not kill the people. 52 bullets out a machine gun is not so much. a 0.50 caliber machine gun can fire 50 rounds per minute. And if these guns were aimed at the fishermen, sure all of them will be dead with multiple gunshot wounds. The bullet hitting one fisherman only once was an accident. An accident which happened in self defense as the Taiwan boat tried to ram the coast guard ship so that the other boats can escape. The coast guard ship is not a navy ship. It is a apeed boat roughly the size of the Taiwan boat. There is a video and after the investigation, it will be released.
3. The Philippine Navy was reported in Taipeh and Beijing as the one behind the shooting. The Philipine Navy denied it because all of their ships at that time was docked. Later The Coast Guard admitted that they were involved in the incident. That is contrary to what most Chinese believed that the PHgovernment first denied then admitted to the shooting.