ID this small plastic object?

Interesting. My roommate had it among her assorted misc. nails/screws/anchors but couldn’t ID it.

So, we have a brick and mortar interior above the fireplace, and wanted to hang an item (off to the side, away from any potential heat, but bear in mind we live in Texas so fireplace use will be almost nil) and there are one or two pre-drilled holds in it. If it fits tightly into one of them, can we use this thingie? (Well, plus the actual screw.)

Sure. You need to push it into the hole with some force, but not too much or it could crack the brick when you drive in the screw. If the item is not very heavy there’s not much to worry about.