I was unable find any "BIRTH DETAILS" in familysearch other than the Census records.
No, you wouldn't. FamilySearch does not have this information. As I said above, the IGI (FamilySearch) is an
INDEX only. (and a very useful finding aid it is too for the period from 1855 to 1874). However even the census information on FS is only a transcription of the original. The originals contain a lot more information than either the indexes or the transcriptions
The only source of original birth, marriage, death and census documents is Scotland's People.
So as I had "Marion Inglis Miles" full name and birth I went to scotlandspeople and put Marion Inles in the first name only. I only found one person with first name as Marion Inglis married in 1930's so I purchased the information but could not find any connection.
Why did you waste credits on a marriage in 1930? If you knew from FamilySearch that Marion was born in 1872, you would have been able to work out that this Marion Inglis was almost 60 years old in 1930, so was unlikely to be the one you are looking for. (She could be a granddaughter of William Miles and Mary Wilson.)
The information on William Miles and Mary Wilson of Stonehouse and their family is very sparse.
Only because you are not looking in the right place, which is
www.scotlandspeople.gov.uk.
From the Scotland's People index, Marion Inglis Miles died in 1947, aged 76. Her death certificate will tell you whether or not she was married, and if so who her husband was; exactly when and where she died, and tha cause of death; the names of her parents and who registered the death.
Mary Wilson or Miles died in 1916, aged 70.