Item Number 3
One of my favourite designs is found in the 3rd Shahsavan bagface shown in the Kaffel salon.
The piece is unbelievably beautiful and, with a red field, would have to be unique. A truly amazing piece.
I have an old, very worn fragment that has the same field design, this time on a blue field.
As you can see the top and bottom borders are missing so I do not know if this is a bagface or an end panel from a mafrash. I am pretty sure it is a bagface. With the borders included it would be longer than wider. Also, the majority of end panels do not have side borders ....I think.
The third image is a Varamin Luri? bagface.
As you can see, the design is very closely related, but this piece is not Shahsavan.
I am intrigued by this design and would love to learn more about it.
The design you have shown is known as the "spanner" motif.
It resembles a wrench. Probably derived from early 15th century Armenian wrench designs making their way into textiles. Possibly Mother Goddess wenches, too.
(Oops, I mean wrenches)
I, too, think your third example is likely Varamin due to the motif at the bottom. Note that this and the second weavings have the "S" in a cartouche.