Yes, I see that you have a lot more information than you originally stated, and the inclusion of Adam Hay as a witness does strengthen the case for Alexander being related to at least one Adam Hay.
You say that George was baptised by Bishop Skinner (See
https://en.wikipedia.org/wiki/William_Skinner_(bishop). This is quite significant, because it means that they must have been adherents of the Episcopal Church. The generally available baptism and marriage records are the registers of the Church of Scotland, the Roman Catholic Church and some of the minor, mainly presbyterian, churches. In theory the C of S was supposed to record all baptisms and marriages irrespective of which denomination the people belonged to, but this did not always happen.
So if I were you I would be trying to find out whether the relevant Episcopalian registers have survived and if so where they are. If they are available, they could possibly contain information about the marriage of Alexander Hay to Grace Farquhar, the baptisms of George, Jane and possibly intervening children, and the deaths of Grace Farquhar and Marjory jr.
I would start by contacting the Episcopal diocesan office of Aberdeen, the Aberdeen Archives and the Aberdeen University Archives.
You are right that adults' ages in the census were rounded down to the nearest 5 years. Unless there is an error in the FreeCEN transcription (Have you seen the original? What does it say?) which lists her age as 30, Marjory cannot be as young as 25. She has to be between 30 and 34 years old, in other words born between 8 June 1806 and 7 June 1811.
I would not place too much reliance on ages reported on death certificates - they can be out by several years. Children's ages, even in 1841, are more usually correct. Do not dismiss the possibility that Jane and Marjory Jr are two different children.
The wording of the baptism of Marjory is of exactly the form used when the
recording of a baptism has been delayed, and the parents can remember when the child was born but not when he or she was actually baptised. I would read it as saying that Marjory was born on 5 October 1838.
Now for a bit of speculation. I note that according to the 1841 census (FreeCEN) Alexander was born in Aberdeenshire and Marjory was not.
Noting that the IGI lists four children of Adam Hay and Margaret Bruce
Adam Alexander, baptised 1838
James, born 1855
Joseph, born 1857
Margaret Andrew, born 1861
that the 1841 census (FreeCEN) lists
Adam, tailor, 25; Margaret, 25; William, 5; Adam, 2; and George, 1
that the 1851 census (FreeCEN) lists
Adam, tailor, 38, born Turriff; Margaret, 36, born Banff; George, 11; Alexander, 8; John, 6; Leslie, 4; Ann, 2; Burnet, 6 months
and that the 1861 census (FreeCEN) lists
Adam, 48, tailor, born Turriff; Margaret, 46, born Banff; John, 24; Leslie, 14; Ann, 11; Burnett, 9; Duncan, 7; James, 5; and Joseph, 3
I am wondering if this Adam and Margaret could be a brother of Alexander and/or sister of Marjory. If they were, and they were Episcopalian, it would acoount for all those children missing from the baptism records. At the very least, I would want to take a look at the birth certificate of James in 1855.
Obviously, if Adam was a tailor, he isn't the labourer who was a witness at whichever baptism. That could have been the child's grandfather.
I also see that Marjory is named as Marjory Hay, previously Ross, M S Bruce. Could Jane be a daughter of this previous marriage, adopted at such a young age by Alexander that she believed herself to be his biological daughter?
