From Kamikazes to propaganda and psychological warfare, why did they deserve the atomic bombs? How effective were their war methods against the US?
Whether Japan "deserved" the atomic bombs is a matter of opinion, not objective historical fact. Besides, the U.S. decision to drop the bombs was motivated primarily by war strategy, not some sort of sense of moral obligation to "punish" Japan. The dead of Hiroshima and Nagasaki were not the first Axis civilians to be killed by the Allies for the purpose of strategy and expediting the end of the war.
Japan's vision for the war was to establish what they called the "Greater East Asia Co-Prosperity Sphere". Basically, Japan wanted to conquer eastern Asia and turn it into an empire ruled from Tokyo. Japanese propaganda claimed that they were "freeing" Asian countries from Western imperialism, hence their slogan "Asia for the Asiatics". In fact, the concept of the Greater East Asia Co-Prosperity Sphere was hierarchical, with the Japanese at the top and non-Japanese Asians regarded as second-class citizens.
Japan didn't have designs on the U.S. itself, but the Philippines were a U.S. colony at the time. This meant the Greater East Asia Co-Prosperity Sphere would represent a threat to U.S. interests. The Japanese strategy when they bombed Pearl Harbor was to deliver a devastating blow to the U.S., from which the Japanese could negotiate from a position of strength and force the U.S. to stay out of their way in Asia.