Should I just throw this out? Damaged Bisque thing-a-majiggy Thanks!

I have had a bad month cleaning out the attic junk. Earlier this month I discovered I threw out an 18th century Worcester cup. Hoping to avoid future disastrous decisions by posting the items before I toss them. As you may deduce, I know nothing about porcelain or pottery! Thanks for your help!

 

Is it possible to turn your head like that?

 

No idea who the maker is. I do like this thing, though it looks a bit bizarre to me. The damage will seriously affect the value. Has the head been re-attached?

 

I apologize for the late post...storm Henri was flirting with us yesterday. The head has not been repaired. That is the normal stance. Odd, isn't it? Her bowl is broken and reglued, a ribbon on her head is chipped off as well as a finger. I have been trying to determine what the purpose of this was. I am not familiar with a torch like cork as shown. I am stumped! Thank you for replying!