I have been unable to find more about Robert after brother Tate's estate settlement in 1837. Several people identify him as the Robert Alexander who died in Hendricks County, IN, in th 1860s, and others name him as the Robert Alexander who died in Iowa 29 November 1862Note 1. Make your determination by a look on Find A Grave. I have not addressed Robert further.
Although Tate's will and estate settlement provided lots of information about the family, little more is known about his life except his appearance on the 1830 federal census in Burke County alongside his brother John.Note 2
In 1820, Joseph and wife appear on the census on the same page as Samuel Dysart. Both Joseph and wife were over 45, and had two males between 16 and 26 in their household. The two were probably Tate and another of the younger sons, most likely John P., since I cannot find a marriage for him until 1828. There was a Samuel Alexander on the 1820 census listing his age as over 45, and, if he was Joseph's and Margaret's son, he was apparently born early in their marriage, not later than about 1775.
There is also a William Alexander on the 1820 census in Burke County. He and his wife are between 26 and 45 and have two males under 10, five females under 10, and one female between ten and 16. This fits Joseph's and Margaret's son if some of the older children were gone from the family by 1850, which seems likely.
I have found no census listing for Joseph Lowery in 1830; therefore, he was probably deceased. I have not found Margaret as head of a household in 1830, and although females were not listed by name unless they were head of a household, I have not found anyone who seemed likely to be Margaret, meaning she was likely dead also.
1820 Census (Joseph Lowery): "United States Census, 1820," FamilySearch (https://familysearch.org/ark:/61903/
(Samuel) "United States Census, 1820," FamilySearch (https://familysearch.org/ark:/61903
(William) "United States Census, 1820," FamilySearch (https://familysearch.org/ark: