i suppose it could be used as a door hanging but door hanging is called Kupunik I think jollar is the term used your textile pic ..here's a pic of kupunik that hangs above the door
An ensi is a door covering for the outside looks like this is this one is a hatchli design and NO it is not a prayer rug even though it look like one
germech are very rare and they are no wider and often not as wide as ensi and are bottom door covers to keep dust out of yurts