Rear hub-adjuster thing - What does it do?
The dangly adjuster thing is most likely the toggle chain for an internally geared hub!



The tension on that chain shifts the hub internally (rather than through a derailleur and cogset). Bike hacks with three-speed hubs are quite common, but get very complicated. Here is some information on Sturmey Archer hubs courtesy of Sheldon Brown. 

Below is a picture of the toggle chain and rod which is attached to the inside of the hub. Good luck!