Birth certificates did not exist until the start of civil registration in 1855.
Before that, the only records are the churches' records of baptisms, which sometimes but not always give the date of birth as well. However there are many gaps in the parish registers.
I think there was a fire at Brechin at one point and I wonder if that’s the reason there are no birth certificates for .... Andrew.
Highly unlikely, because the Farnell church records would have been in either Farnell or (after 1855) in Edinburgh and would not have been affected by a fire in Brechin.
As for Brechin itself,
https://www.nrscotland.gov.uk/files//research/list-of-oprs/detailed-list-of-old-parochial-registers-of-scotland.pdf confirms that the relevant parish register survives.
There are many reasons why a baptism record may not have survived, including
- the parents may have neglected to have the child baptised or to ensure that the baptism was recorded
- the parish clerk may have forgotten to record it
- the parents may have belonged to a different religious denomination; there was, for instance, an Episcopalian congregation in Brechin whose records are not on the Scotland's People web site
Scottish death certificates normally state the full names of both parents of the deceased.
Have you seen the death certificates of Andrew Ferrier and Maria Ferrier? If not, that is your next step. If so, what do they say?
Andrew Ferrier, aged 64, died in Arbroath in 1885, mother's maiden surname Fraser.
Maria Sutherland, aged 56, died in Marykirk in 1877, no mother's maiden surname indexed.
Both available to view at
www.scotlandspeople.gov.uk