You're good! I'm confused by the "B.R.", but this looks interesting. Wouldn't be the first "typo" on a census, I suppose.
I'd seen some research leading me to believe that William C.'s grandfather (John, b. 1765) married a gal by the name of Parker. It appears in this Iowa census there is a Parker living with them.
Now, I'm not 100% sure who William's (Sr) parents are, so I'm not sure if I'm on the right tract. Do you know anything about this line or others that came from Vermont during that time period? If so, I'd love to hear what you have! I also gathered from census data that they spent approximately 5 years (give or take) in Rensselear County New York before settling in Iowa. The 1870 census has them in Durant, IA, and then the 1880 census has them in Sheldon, which is where he died.
Are you related as well?
Thanks so much for your response.