• UH: If it's outer 炉 corner in 炉, it's 本仕舞い; if it's the inner corner, it's 中仕舞い. (This applies only in the large room.)
• If the room is 4.5 mats or larger, it depends on the 点前, if it's smaller, it's always the inner corner and always 本仕舞い.
• If you can use one hand to move the 茶碗, you can do 中仕舞い (technically, you could move it with one hand for 茶入飾 etc, but they are on the same level as 茶碗飾, so that's that; HS 22).
• 本仕舞 is the 'proper way', because things go back to whence they came; and 中仕舞い is the 'informal', or 侘び way, because we allow for this imperfection 😍 Because of this, we compensate the small room's 侘び-ness by finishing 本仕舞い; and tone down the large room's style by sometimes finishing 中仕舞い (HS 22)

is this by any chance the latter 8 of 子習い?

Also, 長板 and 台子 close 本じまい; and for 運び, it seems you can choose (if you are in a 4.5 mat room, obviously). Also, 四ヵ伝 are 本仕舞.