I believe I can answer some of your questions.My gr,gr grandfather was Joseph Twining, a brother of Jacob Twining.Two of the names, Joseph and Thomas, were sons of my Joseph and both served in the Civil War. Thomas survived and later moved with his family to Michigan. Joseph died in the War and is buried in the Van Horn Cemetery in Hancock Co. Henry Clay Twining did not serve in the War, being too young probably.The other Twinings are probably all related as all came from Bucks Co.,PA.in the early 1800's
I have zeroxed some pages from the book, The Twining Family by Thomas Jefferson Twining, published 1905.I no longer have access to the book, but am certain it would clear up some of the other names you mentioned.
What is your connection to the Twining line? I am originally from Hancock Co., but living in Columbus now.Will be going to Hancock Co. tomorrow for a family reunion on my mother's side. Maybe I will be able to find more with a little more research.Let me hear from you.