As yet, I cannot confirm or otherwise the true maiden name of Mary. In 1851 Census they have 6 children. Most trees I'm able to view have it as Cook though, I must be wrong.
I admit that the search for a Mary Bayram (found having moved to Liverpool) b. 1876 and her family has taken up much hair pulling of late.
As for the father of John, b. 1774ish, I have him married to Elizabeth Marshall and that's all at present.
I shall have to delve deeper and post as necessary.
Sorry I can't be of much help at present, Andrew.