I downloaded multiple icon sets to work on in Adobe Illustrator, but when I open up the sets, there is only one layer and the icons are not able to be used individually. I have tried to ungroup them and I have also tried to release any settings that could be affecting the layer. However, since there is only one layer, I have a feeling this is more complicated. How can I use the icons in the image individually? I have googled and searched everywhere for an answer, and I cannot find one—please help!
They are probably inside of a clipping mask or even possibly set as one compound path. Do a command Y and you will likely see a mask path outside all of the icon, drag the direct select tool to get the mask then delete.
You can then drag with direct select tool to drag a frame over the icon you want, cut that and paste into a new document is the easiest way though there are many methods.
If you need more help please post a screenshot of the item selected and the appearance palette so we can see what you have.
Your "editor icons.jpg" shows the file with an Adobe watermark, it looks like all you've done is download the preview, which is NOT editable vector art... you have to BUY a license for the editable icon set...