Short answers, pulled from the story.
Princess Mononoke was released theatrically in Japan on the 12th of July, 1997. It screened at 260 of Japan's 1,800 cinemas and drew over 14.2 million viewers within a year of its release, making it the highest-grossing film in Japanese history at the time.
Princess Mononoke was written and directed by Hayao Miyazaki. It was produced by Toshio Suzuki, animated by Studio Ghibli, and distributed in Japan by Toho.
Fantasy author Neil Gaiman wrote the English dub script. He was recommended for the role by director Quentin Tarantino, to whom Harvey Weinstein of Miramax had first offered the job. Gaiman made significant alterations to the script to bridge cultural differences for American audiences.
Princess Mononoke is set in the Muromachi period of Japanese history. Miyazaki chose this era because it represents the historical moment when, according to animation writers Jonathan Clements and Helen McCarthy, "humankind pushed nature into submission."
The score was composed by Joe Hisaishi, a longtime collaborator of Miyazaki's. The final score was performed by the Tokyo City Philharmonic Orchestra, and a third version arranged for symphony orchestra was performed by the Czech Philharmonic and released in 1998.
Miyazaki composed the first preliminary concepts in 1980, seventeen years before the film's 1997 release. He began formal work on the project proposal in August 1994 and commenced animation production in July 1995, with storyboarding continuing in parallel until January 1997.