So family names match, ages match they were in the same locations at the same time but to confirm 100% I need to find there births.
I've been mulling over this, and I'm not sure that finding their births will actually prove conclusively who was who.
You have evidence from the 1841 and 1851 that they were all born in Midlothian, and you also have evidence from the 1841 for the children's years of birth (except John, who was not listed with his parents and siblings). From the 1851 census, you have evidence for more precise years of birth for George and Jane/Jean/Jan(n)et, and confirmation that they were born in Midlothian, possibly Edinburgh.
If any of them had married in Scotland after 1855, their marriage certificates would have provided definite evidence because Scottish marriage certificates give the full maiden names of the couple's mothers. But without knowing Jane/Jean/Jan(n)et's surname from other evidence even that wouldn't be proof.
I looked to see if Susannah Muir, née Patterson, had died in Scotland but that does not seem to be the case. It would be possible to find out whether her husband died in Scotland, but a bit time-consuming, especially if he didn't, and with the eight-year discrepancy between his DoB as stated in your first post and his age as recorded in the 1881 census. 73 deaths of John Muirs born between 1821 and 1831 were registered in Scotland after 1881.
