In regards to the census in 1861, I also think that Alexander, Christina & James Brown are actually the McFadyens. This is largely based on following the movements of James Dewar Brown.
We all seem to agree that James Dewar Brown married Agnes Beveridge in Newton in 1835. The marriage record says that she was from Squaretown in Newton. According to the National Gazetter in 1868, Squaretown is in the parish of Newton, as is Edmonstone. James Dewar Brown says that he was residing in Airdrie, which is located in Lanarkshire, and he was a collier (coal miner).
In 1841, we think that James, Agnes, Isabella and Christina are living in Coathill in the parish of Old Monkland, which is only about 5km from Airdrie. James is a coal miner. This matches perfectly with the marriage and links us to Christina. Only Isabella was born in the county of Lanarkshire.
In 1847, Isabella Brown is residing with her brother, James Dewar Brown, miner, in Airdrie. This matches James' name, location and occupation of the 1841 census. James and Agnes likely named their first child after his sister (which also makes it likely that both Isabella's are named after another relative such as mother or grandmother but that's research for another day). The source for that is the Airdrie Sherrif Court decrees.
In 1851, James Dewar Brown (indexed as James Dewan Brown on Scotland's people and James Dowar Brown on Ancestry) is living in Old Cumnock, Ayrshire. He gives his place of birth as Edmonston, Midlothian and says that he's 40 years old and a coal miner. This matches the age and occupation of James Brown in 1841 and the location and name in 1847. The birthplace is critical because Edmonstone is a village in Newton, which links us back to the marriage and how he may have known Agnes. The name and age match the marriage, 1841 and 1847 information. The reason against this being our James is that on this census is Elizabeth Brown, daughter, aged 16. This would mean that they were interchanging Elizabeth and Isabella - which is not uncommon but it is the only place it happens. Also, the place of birth is given as somewhere in Midlothian - but I can't read it (It's transcribed as Ruthin but could even be Preston when looking at the original) However, in 1861, James' information remains the same and Elizabeth is listed as Isabella again. Christina is not in the household in 1851 and I have not been able to locate her.
In 1859, Christina and Alexander marry. Christina gives her parents as James Brown and Agnes Beveridge, matching the marriage we have in 1835. Agnes is deceased which matches the 1851 census entry. I think the is witnesses J.D. Brown although you have I. D. Brown. So either James Dewar or Isabella. This witness signs their name, as does Christina. Alexander is the only one who has an x for his signature. James is an Ironstone Miner, when in all previous records he is a Coal Miner. However, in the 1861 census, he is also a ironstone miner.
In 1861, James Brown, is living in Crofthead in the parish of Whitburn, which is approximately 22km from Airdrie. He is 52 years old, widow, born in Edmonston, Midlothian and a ironstone miner. This links the occupation stated on the marriage, and the place of birth and age in the 1851 census. Isabella is in the household as well, stating that she is born in Airdrie. This matches the 1841 census, and she would have been born close to James' residence on the marriage certificate and the residence in 1847.
Given that we can follow the path of James Brown in the primary sources, it seems highly unusual to me that there would be a completely different Alexander, Christina and James living as boarders in the home of James Brown.
Rona