Short answers, pulled from the story.
Government troops fired directly into a crowd of Buddhist demonstrators on the 7th of May 1963, killing nine people and injuring four others. Two of the dead were children crushed under armored personnel carriers while Major Đặng Sỹ ordered his men to launch grenades and firehoses at the protesters.
Buddhists protested because the government invoked Decree Number 10 on the 7th of May 1963 to prohibit the display of Buddhist flags on Phật Đản while allowing Catholics to fly Vatican flags for Thục's anniversary. The regime also pursued pro-Catholic policies that favored Catholics in public service, military promotions, land allocation, and business favors.
The deputy province chief in charge of security, Major Đặng Sỹ, enforced the law on the 7th of May 1963 as commander of the Huế garrison. The origin of the order has been attributed to Ngô Đình Thục, the Archbishop of Huế and brother of President Diệm.
Thích Trí Quang proclaimed a five-point manifesto on the 10th of May demanding freedom to fly the Buddhist flag, religious equality between Buddhists and Catholics, compensation for victims' families, an end to arbitrary arrests, and punishment for officials responsible. A delegation presented these demands to Diệm on the 15th of May during a meeting at Xá Lợi Pagoda.
U.S. Ambassador Frederick Nolting attempted to spread responsibility among all parties while claiming the demonstrators tried to take over the radio station. After six months of tension, American diplomatic staff led by William Trueheart ended the policy of appeasing Diệm following Nolting's departure for vacation.