Short answers, pulled from the story.
Sophie Hatter is transformed into a ninety-year-old woman by a curse from the Witch of the Waste. This transformation serves as the catalyst for her journey to the moving castle and redefines the boundaries of age and self-worth.
Calcifer is a fire demon whose existence is inextricably linked to the wizard Howl's own heart. He powers the castle's movement and his life depends on Howl's heart, creating a bond of mutual dependence.
Hayao Miyazaki created the 2004 film Howl's Moving Castle as opposition to the United States invasion of Iraq in 2003. The film reflects his anti-war themes and concerns about the futility of modern warfare.
The true form of the Witch of the Waste is a powerful decrepit old woman. Her power was drained by the King's head sorceress Madame Suliman, reducing her to a harmless and very elderly state.
The 2004 film Howl's Moving Castle ends with Sophie placing Howl's heart back inside him to revive him and free Calcifer. This resolution symbolizes the interconnectedness of all things and the power of love and understanding to redeem flawed characters.