Stephanie,
Birth registration didn’t start in Ireland till 1864 so finding Theresa Hastings birth may be challenging. Pre 1864 we rely on church baptism records but they don’t all exist, and even where they do, they are not always on-line.
I can see that Theresa married in the Church of Scotland. Was she baptised a Presbyterian? Or were her parents a mixed denomination relationship?
In the 1881 census Theresa’s place of birth is given as Ochiltree, Ayrshire but in 1891 it is Ireland. Suspect the 1881 may be a mistake. I don’t see a birth for her in Scotland on Scotlandspeople, so assume she was born in Ireland.
Did Theresa’s parents have any children born in Scotland, 1861 onwards? If they did, the birth certificates should record where and when the parents married (assuming they did marry), which would be a great help.
Did Margaret Hastings marry in 1871 to a John McFarlane in Sorn? If so, I note she said she was a spinster then. Aged 50. So maybe she never married Theresa’s father? Margaret’s death certificate makes no mention of being born as Beck. Her parents names are given as Hastings (John Hastings farmer, deceased & Janet Hastings ms Hastings deceased). Informant was Theresa who presumably knew the facts. Possibly Theresa was illegitimate? Father;s details created for the benefit of her marriage?