I think both of you have got the gist of the song.
I can add that 'coolie red' is a cheap cloth worn on their heads by East Indian immigrants, who were called coolies in the BWI.

A ten penny nail is 3 inches long. (a 6 penny nail is two inches long).
A nail should be three times as long as the wood it is holding. Two-thirds of its length should be driven into the other piece of wood for proper fastening.

When I was a child, bulk containers for nails were common in stores. One filled a sack with the size desired and it was weighed to determine the price. The penny" designation used to be common. Smaller nails were designated by their actual length.