The Brazos River has three forks: the Clear, the Double Mountain and the Salt. Regardless of what fork it was found on, that rock in the first two photos is just a rock. Other than NE Texas, polished celts or axes are a rare item in Texas.
Eric, It was great to meet with you and M. on 3/22, and really enjoyed seeing some of your artifacts.
The broken San Saba appears to be exactly what you have identified it as, and Redman may be right about the rock, as he is also very good with identifications.
However, many rocks like this were actually used without being altered in any way from their original form. If a trained archeologist had picked this stone up on or at an identifiable campsite, it would have likely have been recorded as an artifact. Why?......
Well, stones shaped like this one were used to stretch animal hides around to make moccasins (foot wear) and small pouches. So, that makes it a potential artifact that we will probably never know a definite answer on. Just thought you would be intrested in the additional comment.