布団 and 枕: laying out and putting away bedding
Name bedding and pillows while separating preparation from use.
Laying out bedding
布団 (ふとん) refers to bedding such as a quilt or floor mattress. 「床に布団を敷きました」 describes laying out bedding to sleep on the floor.
「布団を掛けて寝ました」 describes sleeping with a quilt over oneself. The verb helps distinguish bedding laid underneath from bedding used as a covering.
A pillow for the head
枕 (まくら) means pillow. 「枕の高さを変えました」 says the pillow's height was changed.
「枕元に時計を置きました」 means putting a clock by one's pillow. 枕元 (まくらもと) is not restricted to the pillow's top surface.
Preparation versus sleep
「布団を敷きましたが、まだ寝ていません」 says the bedding is laid out but the speaker has not slept yet. Completed preparation is not completed sleep.
「起きてから布団を畳みました」 places folding the bedding after getting up. 畳む (たたむ) means folding something up.
Does 「布団を敷きました」 say the speaker has already fallen asleep?
Show the answer and why
No. It describes preparing the bed. Falling asleep requires separate information.