got a set of profile design bull horns and fitting an aero lever/tt brake.
name this one
how is this inserted into the handlebar and how does one adjust?
These are generally inserted in the location where the bar end plus would go. Most if not all of these levers have a rubber plug at the front that you remove to reveal a bolt that you will need to turn to tighten itself onto the inside of the handle bar.
Adjust the brake cable? You could use an inline adjuster. http://pbkmedia.probikekit.com/catalog/product/cache/18/image/420x460/9df78eab33525d08d6e5fb8d27136e95/1/1/111124.jpg