The answer to both of your questions is that I cannot readily identify all of the Broaddus and Pullers whom you inquired about; however, I do have some suggestions.
1. The identity of Catherine, the wife of Wm. Dandridge Puller, as a Broaddus rests on no firmer ground than that Broaddus was pencilled in after her first name in the Puller Family Papers (tax records), which are on file at the Library of Virginia. My guess is that she was a daughter of Richard Broaddus, who acquired the Fork Quarter Plantation in King William County from Col. Wm. Nelson, in 1801. This might explain why Wm. Dandridge Puller and Catherine lived in King William County until his death, in 1828. It would also explainwhy one of their sons was named Richard A. Puller. Apparently, Catherine moved to Caroline County after the death of Wm. Dandridge Puller. In 1839, the estate, in Caroline, was divided among the heirs, who included Thomas B. Puller and Elizabeth C. Puller, in addition to Richard A. Puller. Another heir, who was not listed, was Mary Cornick Puller Thomas, the wife of James Thomas of Richmond, a very wealthy tobacco merchant.
2. I am not able to identify James Puller, who married Mary Broaddus. Caroline County Land Taxes showed that James was deeded 244 acres by Mordecai W. Broaddus, in 1837; and he appeared in all subsequent Caroline Land Tax lists through 1840 (no later years were included in the Puller Family Papers). His name was not included among the heirs, receiving land from the estate of Thomas and Sally Puller, in King William, but all of the King William land was not acounted for in the record of the distribution; and it may have been because James and Ellen were too young. Parkinson may have been the middle name of the William listed in the Puller Family Papers as William E. Puller. It is possible that an error was made in reading or in transcription.