After a goal, the thrower-in can run the endline, and/or pass to a teammate also out-of-bounds (release within 5 seconds).
Can he dribble along the endline (I mean with the ball totally out-of-bounds)?

Dribble and travel rules do not apply during a throw-in.
Yes, what you ask is legal.

To expand on Dan's perfectly correct statements...
 

Which is to say that the limits defined in the traveling and dribbling rules do not apply during a throwin. A thrower may legally run/move (within the designated spot area if applicable) without dribbling. They may also legally dribble, catch, dribble, catch... They may legally carry the ball while dribbling. It is not possible to have an illegal dribble or traveling violation on a throw-in. As long as the throw-in is released in 5 seconds, there are few limitations.