All of the scholarship finds the Jewish burial requirements hold that if there was a shroud used, the face was not covered by a separate cloth. However the cloth here was used as a kerchief like rope to tie the jaw closed, and was wrapped AROUND the face. . . under the jaw, passing under the beard, behind the ears and hair, and then being tied above the crown of the head. i.e. around and about the the face to keep the mouth closed in death, otherwise the mouth would gape open. Similarly a coin or potsherd would be placed to weight the eyelids closed (such coins or potsherds are often found in the eyesocktets of skulls). Also the wrists and ankles would be bound with a similar cloth strip of binding to keep them from flopping akimbo when rigor mortis passed. These practices are documented in Jewish writings of the period.
If no shroud were available small cloths and modesty cloths would be used, but cloth was expensive, representing several days to weeks of work by skilled craftsmen and women to produce.
Yes, it was. Good point.
I can better understand the part in the Gospels where there executioners chose to draw lots for Jesus' tunic, because it was seamless and woven from a single piece of fabric. They said they didn't want to tear and divide it into four pieces.