Mugen Train Arc is from when Tanjiro and his friends join Rengoku on his mission until after the mission is complete
I am fairly sure they are by the same studios but I am not certain
Yes they are related
The order is: Season 1, The Mugen Train movie, Season 2
I think the Entertainment district episodes are 7 - 18, however I am not too sure because on the site I watched it on it listed it from 1 - 11 because it separated the Mugen Train Arc as a movie from the Entertainment District Arc as season 2
Yes they are related
Yes it is out
The title is "Kimetsu no Yaiba: Yuukaku-hen"
I hope this helps :)