Since Mud Hut and nhbenz have already correctly identified the bustier/corset closure clip, I'll tackle the "brass ring."
It does resemble a sawed-off section of a threaded civil war artillery fuzeplug. But to be certain, I'll need you to provide precise measurment of its outside diameter and inside diameter. Also, need a photo showing the other side of it.
I can't for the life of me figure out the reason for doing it, but more than just a few examples of sawed-into-pieces brass artillery fuzeplugs have turned up at civil war sites. Having seen quite a noteworthy number of examples, I have no doubt that somebody was doing it during the war. I just can't figure out why. The only logical answer that comes to me is, the cut-to-pieces fuzeplug parts were going to be adapted for some other function. That function is the mystery.
It'd also help if you have access to a Thread-Gauge. US Hotchkiss and CS timefuze-plug threads are 12 threads per inch. The yankee Schenkl fuze had 10 threads per inch.
For anybody here who doesn't already know:
Yankee fuzeplugs were made of typical "yellow brass." Confederate fuzeplugs tended to be made of a high-copper content alloy of brass... which has an orange-ish/golden or pink color, depending on how high the percentage of copper in the alloy with the zinc. (Typical yellow brass is about 70% copper with 30% zinc... and what is called "red brass" is 90% copper with 10% zinc.)