It didn't say the ?Falstons are children of Williams.It just said they lived there.They might be nephews or family friends.Just as in the 1860 census with Alex Nails.He might be a brother to Malinda.When someone with a differnt last names might means some kind of relationship.This might give a hint as to Malinda's maiden name.
It appears as if William is on his second wife named S. L. You can tell because she's from Mississippi and Melinda is from North or South Carolina.I would say NC because of the 1900 census.S.L. wouldn't be the mother of Mary.
As far as William's middle initial, it defintely was an "F" on the census record in 1860.I looked at a list for his name in the 1880 census and it was someone else who intrepreted it as a "T".
Usually, the census taker spelled the names as they sounded so there are going to be a lot of mispellings.
If your new to this go to www.rootsweb.com and go to the beginner's page.Or go to www.familysearch.com.Both will explain how to approach your search for your ancestors.