Members of the Archer, Collins, Adcock and Fletcher families did migrate to the Oklahoma Indian Nations and there are many applications made by family members trying to gain recognition.However I have yet to find one application which was accepted.That is not to say that I don't think they had Indian heritage because I think there is a great possibility/probability that they did.They were just unable to prove it at that time.
I don't think any Shewcraft/Showcraft families migrated to OK.I know the line I have researched moved from TN into TX in the early 1890's and died there.If you look at the census records in TN from 1820-1900 you will find very few people named Showcraft (of any spelling).So that family group seemed to be very small, unlike the Collins, Nickens and Archer families who were numerous.
Now to answer your questions. (1)All of the Adcock families I have researched appear to have no Indian heritage of any kind, except for the children born to the Adcock families who marred into one of the above mentioned families.In the application of Mary Jane (Collins) Adcock, she indicated that she thought her husband James A. Adcock claimed some Indian blood, but that is the only time I have seen that mentioned.And I know that James A. Adcock and none of his brothers or sisters made applications for Indian recognition.If James did claim Indian heritage, then it may have come through his mother, Frances "Fanny" Nickens who first married a Shoecraft, then an Adcock, then a Collins.I have not really researched the Fletcher line, but a distant cousin has worked on that line and she has not come up with any indication that the Fletchers had Indian heritage. (2) I have not worked on the Foreman family at all since the Foremans have not married into any of my Collins, Scott, Nickens, Showcraft, Archer or Adcock lines.So I really can't help you with that family.
Thanks for contacting me.If you have any other questions just contact me again and I'll be happy to answer them if I can.