Roman silhouette, Greek bowls?

I bought a few items that were framed in shadowbox frames. I took them out of the frames and there is some residue and staining from the glue-like substance that held them. There is a little carved piece of alabaster with a silhouette, only about 2x2.5". What do you all think.....is it old? Should I try to clean it? The other pieces are old pottery bowls that could be Roman or Greek. They were inexpensive. Thank you for your thoughts.

 

Figure on fragment looks like the goddess Artemis/Diana.



I would look to Greek red & black pottery for the footed, handled bowl.

 

You might research using the term kylix for the bowl.