The movie is basically season 2, but after the movie release they made an episodic version of “season 2” which includes some additional story at the beginning, with most episodes after just being an edit of the movie. I’m sure other commenters can provide specifics on which episodes to revisit after watching Mugen Train.
Best way to do next season is to start with season two episode one and then the movie followed by episode eight to keep the story moving forward in my opinion.
I think most anime movies that are part of a running tv series just say “fuck it. If you didn’t watch the show, good luck”. Sometimes they’re canon (Berserk), sometimes they’re just truncated retelling of seasons (Tiger & Bunny), and sometimes they’re just noncanon side stories with the characters of the series at wherever they were in the tv show at that point (DBZ, Naruto), but they always assume you have at least a passing familiarity with the series
Anime is a very vast area, you can't really put it in a cube and just one single category. It can be appropriate to all ages depending on the rating. I worked at a daycare whom my boss had a friend from Japan and she recommended an anime to my surprise was a real hit from the very young to kindergarten, it was called, "Panda go Panda." And I have seen anime that was shockingly inappropriate to any age called, "Ninja scroll." but Demon Slayer (to which I think is a watered down sugar coated version/inspired by Ninja Scroll) is geared towards older teens than for a young audience.
The "cape" that the characters wear is called Haori, it's a traditional Japanese jacket. Regarding the movie, I'm going to recommend that you watch the entire second season (first and second cour) instead. The first cour of the season is basically the movie "Infinity Train arc" with extra scenes and an original canonical episode of the story (episode 1), which from a reaction standpoint is better to watch like that, the quality doesn't degrade (because it's Ufotable) and what's more, it's improved by the dialogues and extra scenes (personally) P.S. The original content of the anime is directly approved by Koyoharu Gotouge author of Demon Slayer. Ufotable studio makes sure that the content they adapt and create for their anime is approved by their authors or the authors' personal associates.
so for season 2, episodes 2-7 cover the events of the movie, with episode 1 being a filler lead-in to the movie's events. you can watch it before the movie, but its not a necessity. then episodes 8 onwards are the next arc of season 2 beyond the movie
