The 1841 census shows James Adam, 63, labourer, not born in county, with Mary Adam, 59, Anne Adam, 36, and James Harlay, 9, all born in Aberdeenshire, living in Newburgh in the parish of Foveran, Aberdeenshire.
The death record you have is not a death certificate. Death certificates did not exist before the start of civil registration in 1855. It looks as if it is the burial record, which is from the Foveran parish register and available from Scotland's People (SP).
The dates on the wills you have found are the dates of death, not the dates of birth, of the persons who has died, so those two wills are not the person you are looking for. I can see only one will of a James Adam(s) who died in 1848. As this James Adam was Town Clerk of Forfar, he is obviously not your one either.
The census in 1841 was taken on the night of 7 June, so if his age is accurate in the 1841 census James would have been born in either 1777 or 1778.
The index at SP lists 12 baptisms of James Adam(s) in 1777 and 1778. One can be discounted as he was born in Forgue, which is in Aberdeenshire, and your man was not born in Aberdeenshire. However you must not assume that the record of his birth/baptism has survived. There are many reasons why his baptism may not be in the surviving records, ranging from poor record-keeping to loss of the registers.
Ignore FamilySearch, by the way. It is a wonderful resource for pointing you towards information, but it has its drawbacks, not least that it is only an index and does not contain links to the original documents on SP.
I see from the baptism indexes at SP that James Adam(s) and Mary Ste*nson had three recorded children
James, baptised 18 December 1802 in Cruden
Peter, baptised 30 August 1811 in Slains
Isabella Gordon, 30 March 1814 in Slains
Cruden and Slains are coastal parishes north of Foveran. It looks as if they moved southwards from Cruden to Slains to Foveran.
View the original baptism records at SP to see if they include names of witnesses to the baptisms who might provide a clue to James' and Mary's families.
The large gaps in the dates immediately suggest to me that there were other children whose baptism records have not survived. There is, for example, a death of Ann Adams or Rennie, aged 88, in Foveran in 1893, mother's maiden surname Stephenson, who is quite likely to be another daughter, and Jean Adam or Wingate, who died in Greenock in 1896 aged 83, mother's maiden surname Stevenson, might perhaps be another. The death certificates should clarify their parentages.
James Adams and Mary Stevenson were married in Cruden in August 1802, so James, baptised 1802, is almost certainly their eldest child, and if so it is likely that his father's name was also James.
Unfortunately the records of Cruden Kirk Session, which might have taken a dim view of baby James' arrival less than four months after the marriage, do not appear to record an investigation into the matter.
Incidentally none of these records mention St Fergus, so what information do you have to link James to St Fergus?