Hi,
Regarding the idea that Michael, John and Edinburgh Laurence were brothers:
I have seen a census with Laurence (M to Martha K) living in Edinburgh with his Uncle Laurence. So I agree with you that Michael and Edinburgh Laurence are probably brothers and have the same father, John Walls Snr. 
However, John (m. to Elizabeth Kirkpatrick)īs death cert shows his father as being called Laurence. (Edinburgh Laurence was born around a similar time so Edinburgh L. cannot be his father) also Michael was born around 1785 and John around 1814, which is an awfully wide gap unless they had different mothers, which we do not know.
Here is some info I found for the Kirkpatricks BTW. It looks like Martha and Eliz were sisters:
John Kirkpatrick
Scotland, Births and Baptisms
Name:   John Kirkpatrick
Gender:   Male
Christening Date:   27 Dec 1812
Christening Place:   , DRYFESDALE, DUMFRIES, SCOTLAND
Birth Date:   20 Oct 1812
Mother's Name:   Janet Kirkpatrick
Indexing Project (Batch) Number: C11820-2 , System Origin: Scotland-VR , GS Film number: 1067958 , Reference ID: 2:160W0H8
Elizabeth Kirkpatrick
Scotland, Births and Baptisms
Name:   Elizabeth Kirkpatrick
Gender:   Female
Christening Date:   29 Dec 1813
Christening Place:   , DUMFRIES, DUMFRIES, SCOTLAND
Father's Name:   Thomas Kirkpatrick
Indexing Project (Batch) Number: C19524-1 , System Origin: Scotland-ODM , GS Film number: 1067959
Margaret Kerr Kirkpatrick
Scotland, Births and Baptisms
Name:   Margaret Kerr Kirkpatrick
Gender:   Female
Christening Date:   13 Feb 1816
Christening Place:   , DUMFRIES, DUMFRIES, SCOTLAND
Father's Name:   Thomas Kirkpatrick
Indexing Project (Batch) Number: C19524-1 , System Origin: Scotland-VR , GS Film number: 1067959 , Reference ID: 2:169B394
Martha Kirkpatrick
Scotland, Births and Baptisms
Name:   Martha Kirkpatrick
Gender:   Female
Christening Date:   14 Jul 1818
Christening Place:   , DUMFRIES, DUMFRIES, SCOTLAND
Birth Date:   12 Jul 1818
Father's Name:   Thomas Kirkpatrick
Mother's Name:   Jannet Keir
Indexing Project (Batch) Number: C19524-1 , System Origin: Scotland-VR , GS Film number: 1067959 , Reference ID: 2:169BGPH
Oswald Kirkpatrick
Scotland, Births and Baptisms
Name:   Oswald Kirkpatrick
Gender:   Male
Christening Date:   04 Sep 1820
Christening Place:   , DUMFRIES, DUMFRIES, SCOTLAND
Birth Date:   29 Aug 1820
Father's Name:   Thomas Kirkpatrick
Mother's Name:   Janet Kerr
Indexing Project (Batch) Number: C11821-8 , System Origin: Scotland-VR , GS Film number: 1067961 , Reference ID: 2:161JW0D
1841 England, Wales & Scotland Census Transcription
Flash, Dumfries, Dumfriesshire, Scotland
First name(s)   Last name   Gender   Age   Birth year   Birth place    
Thomas   Kirkpatrick   Male   50   1791   Dumfriesshire, Scotland   Transcription
Jannet   Kirkpatrick   Female   50   1791   Dumfriesshire, Scotland   Transcription
Margret Kirkpatrick   Female   21   1820   Dumfriesshire, Scotland   Transcription
Oswald   Kirkpatrick   Male   18   1823   Dumfriesshire, Scotland   Transcription
Thomas   Kirkpatrick   Male   16   1825   Dumfriesshire, Scotland   Transcription
Jean   Kirkpatrick   Female   19   1822   Dumfriesshire, Scotland   Transcription
John   Kirkpatrick   Male   7   1834   Dumfriesshire, Scotland
Norma