I watched this movie some time ago and was fairly baffled. Since then I have learned something about the Shinsengumi, so when I watched it again recently it all made a lot more sense.
Some points which might be helpful -
• The Shinsengumi was not a training school for samurai; it was a sort of vigilante police force in Kyoto, dedicated to maintaining law and order and supporting the Shogun. See When the Last Sword Is Drawn for a more conventional view of them.
• The Ikadaya incident, mentioned briefly, was when the Shinsengumi raided an inn and massacred the Ishin Shishi, the anti-shogunate forces from Choshu meeting there; a bloody, violent event, but it did prevent the Choshu men from carrying out their plan to capture the Emperor and burn down the city of Kyoto!
• Apart from Kano and Tashiro the characters are based on actual people, members of the Shinsengumi, who are well known in Japan. They appear in manga stories, a TV series starring young pop singers, and numerous feature films. For a Japanese audience there would be no need to explain who they are and their circumstances. For example, in one scene the Vice-Commander Hijikata (Beat Takeshi’s character) goes to talk to Okita Souji, who is sitting by the lake. He wants to ask him about the swordsmanship of the new recruits, but he starts by asking him, very tenderly, how he is feeling. Okita looks at him without speaking for a few moments, then replies cheerfully that he’s feeling fine. In fact he is slowly dying of tuberculosis, but this is never mentioned; you are expected to know it.
• Kano is the only character who wears white. White is the colour of death in Japanese tradition.
The ending is baffling. It's meant to be. Don't worry about it.
Nothing wrong with the subtitles on my copy, by the way.