秋分の日（シュウブンのひ）: Autumnal Equinox Day (22nd or 23rd September)
秋月（シュウゲツ）: an autumn moon, a harvest moon
秋思（シュウシ）: a melancholy mood (in autumn), somber thoughts
立秋（リッシュウ）: the first day of autumn by the lunar calendar (around 7 August; summer greeting cards sent after this day should carry the greetings for 残暑（ざんしょ）, not 暑中（しょちゅう）)
初秋（ショシュウ）: early autumn, the beginning of autumn
中秋の名月（チュウシュウのメイゲツ）: the mid-autumn full moon; the harvest moon
In autumn, leaves look as if they are burning, so having 火 here makes sense to me even if kanji scholars may not agree with me.