Jon,
These are some quite wonderful rugs! I noticed that a couple of them, #6 and #7, are "cut and shut" where the center section has been removed and the sides were then sewn back together. And most of these rugs show wear at the bottom, in the center, where the flatwoven ends and sections of pile have been replaced. This center section wear and tear must have extended up into the rugs which were "cut and shut' severely enough that the center sections were removed from them.
With so many showing wear in this area, the process by which it occurred was quite likely similar to all of them. In photos of these church rugs that I have seen before, many were hung behind pews and some draped over the front of pews. If hung horizontally over the front of a pew, center wear would have occurred over time, perhaps rendering some of these rugs damaged enough to require the "cut and shut" repairs. If hung behind a pew, constant abrasion from the heads and shoulders of the congregation could have caused the wear in the lower sections. And they obviously didn't ship them back to Anatolia for proper repairs back in the day.
As for your new rug, it looks like a kilim pattern woven in pile. Something is funny about the upper, left corner where it looks like the rug is notched, but that may just be a fold. It appears to be a fairly recent, high quality rug, with a lot of attention paid to the warp bottom ends which were woven into a netting. Romanians have been weaving rugs for many years, as evidenced by the notorious Brasov rug counterfeiter, Tuduc. He went from being a rug repairman in the early 20th century to making entire rugs based on examples in Romania and became a fully fledged faker and famous footnote in rug history. Your newly acquired taste in rugs may provide you with many years of acquisition, appreciation and despair.
Patrick Weiler