Yes, yes and yes. But, they aren't anything like what we generally see used around here. A lot of those quivers say back and were most often used on the belt from horseback. I found them too short for comfortable back use. I do like the bow quivers, however.
In the interest of fairness, my shortest arrow is still over three feet long. Many people that are of smaller stature or who shoot shorter draw lengths (my bow supports up to 36", which is a comfortable draw for me) may find it more useful. I turned to making my own.