I now use the Shorty Ultimate's. Damn fine brake when paired with Swissstop BXP pads. Easy to set up, too. The instructions are a bit silly as they instruct you to set the straddle height in relation to the top of the tyre which means the brake will perform differently between one tyre and another.
As above.
I think it came about when they started getting mounted in the ends of tri/TT aero extensions. Maybe for ergonomics, but it might also have just been done to look better when there is no rider on the bike.. Looks don't matter when your hands are cupped over them though.
There is a fourth type which typically is what you find on an aluminium frame and that is a welded on lump with 3 holes and the counterbore for a shouldered boss
Those bosses with a shoulder are meant for frames that have a counterbore in whatever is mounted on the forks or stays. The shoulder goes into that counterbore if you get my drift. Maybe removing the shoulder using a file/grinder/sanding wheel will allow it to work.