As below, I deleted some vertices and now I have a face (with a strange, dark orange partial outline) that doesn't have any vertices. I'm unable to select the face or manipulate it in any way. How can I select it and delete it? Thank you!
As indicated in comments, the face you're trying to edit belongs to a different object than the one you're editing.
The dark-orange outline indicates that there were multiple objects selected when you edited Edit Mode. If you try selecting multiple objects, you'll see that the last one is outlined in light orange, and all the others are in dark orange. That highlighting remains on the earlier objects when you enter Edit Mode.