Regarding Elizabeth Gillespie, this is her and James Ferguson after their marriage in 1891:
James Ferguson 30, baker, b. Stewarton
Elizabeth Ferguson 24, b. Irvine
Jessie Ferguson 2, b. Stewarton
Cuthbert Ferguson 6 months, b Galson
Address: 18 Orchard St, Galston Ayrshire
With that place of birth for Elizabeth Gillespie, this is the only birth showing in Irvine which would fit:
ELIZABETH GILLESPIE Birth: 24 APR 1866 Irvine, Ayr
Parents:JOHN GILLESPIE and JANET MILLER
As you can see, mother's maiden name is showing differently to what you have.
This looks the most obvious census entry in 1871 for the Gillespie family (name mistranscribed on the index I am looking at) - all the children showing as born in Irvine:
John Gellespie 34, coal miner b Ireland
Jenet Gellespie 33, b. Kilwinning Par, Ayrshire
Margaret Gellespie 10
William Gellespie 7
Elizabeth Gellespie 5, b.
John Gellespie 3
William Cairne 35, lodger
Address: 6 Square, Irvine Ayrshire
Elizabeth's marriage entry to James F. or her death cert would let you reconfirm her parents' details (I assume the death details you put for her were an error - 1887 age 83).
Monica