Hello and welcome to Photrio! It's an interesting question you're asking, and I'm in fact going to move it to a part of the forum where it would fit very nicely.
To further optimize the quality of the answers, it would help to have good (i.e., better) photos of the prints you're curious about. Be sure to not only photograph the print area, but also the edges and unprinted borders (if present). It may also help to have a good photo of the backside of the print, especially if that has some features to it such as writing or stains. Make sure when photographing prints that the photos are in focus, properly exposed (not too dark or blown out) and as evenly lit as possible. Photos that are lit at an angle to show the sheen/surface texture of a print can sometimes help in addition to clear photos without glare etc.
Why do some of our photos like this one, have what looks like when you turn them in the light at the right angle, a metalic sheen in darm parts of the images. But only when you turn them? Is that indictive of a certain time period for American photography?
It's called 'silvering out' and usually associated with insufficient fixing and/or insufficient washing of prints. Storage conditions also likely play a part. Up until ca. 1970, 'plain hypo' fixer was used (sodium thiosulfate), and this fixer was rather slow and with limited capacity. This made this particular kind of defect quite common, especially in amateur prints. Then rapid fixer came along (ammonium thiosulfate), which has higher capacity and a much higher fixing speed, making silvering or bronzing a less common feature. I've had it myself from time to time when I was really sloppy in processing test prints. It's kind of neat, in a way, but technically it's a form of degradation. I assume it's regarded as undesirable in the collector's community and will negatively affect valuation.
As to the era of your print - I'm sure others are far better versed in turn-of-the-century American fashion, apparel etc. But my amateur guess would be your photo is taken sometime around 1890 or so, given the woman's dress. Assuming it's genuine and not some kind of historical re-enactment performed later. This is where good photos of the prints can help a bit.