How are the flat/aero bullhorn handelbars called? I've seen some bikes which look really good (IMHO) with a bullhorn handlebar which is flat and has an aero design.

After some googling I've only found this model which is really expensive:


Do they have some kind of strange name to search them and find something more affordable?

Is it possible to mount normal brake levers in them? (Not in the horns but in the center)

I currently have normal (rounded) bullhorns, but I'd like to get some of this just for aesthetics if I don´t lose functionality.
These are one component of aero bars, used on  time trail and triathlon bars.

These are used in conjunction with elbow pads and bar extensions that mount on top. The attachment points are visible in the pic you provided. 

See this article Selecting the Right Aerobars for Triathlon.

Typically brake levers are mounted on the ends of the lower bars, and gear shifters on the ends of the bar extensions.

Aerodynamic bicycle components tent to be expensive because they are predominately used by pros and racers so they also need to be string and light.