: :Did it fall under the jurisdiction of Cardolan?
: Since Enedwaith, according to Tolkien, was never claimed either by Arnor or Gondor, Cardolan probably took possession of the entire city, including the part which extended into Enedwaith.

: :Was it settled by men from Enedwaith and Dunland after the destruction of Arnor?
: I think it was abandoned. Didn't Boromir have trouble crossing the river to get to Rivendell for the Council?

: Was it originally settled by Dunedain, or the men from Enedwaith and Dunland?
: There very well may have been a pre-Numenorean settelment in the area but I am pretty sure that the city was officially founded by the Dunedain. In the UT Tolkien states that Numenor needed timber for its growing navy, timber which was found in Enedwaith and Minhiriath. (Incidentally, this gave rise to the century-long hatred of the original inhabitants of the area [the Dundlandings] against the Men of the West). My idea is that it was settled some time after the founding of Lond Daer. It is logical if you look at it from this point of view: the foresters cut down trees inland, the trunks are then taken to a nearby camp/settlement (Tharbad) then floated downriver to the port (Lond Daer) where they are used to build ships (it wouldn't make sense to ship the trunks all the way to Numenor and build the vessels there). Tharbad was definitely the scene of a major battle sometime in the Second Age (second millenium, I think).

: :There is much mentioned of Tharbad, and it seems to me that it could have been a major city of Cardolan, and many of the Dunedain could have retreated to it, but nothing is mentioned of Tharbad's importance to Cardolan, and if there has, I would like to here about it.
: It must have been a major city. It may have just fallen into ruin because of the diseases and natural disasters that struck the area in the Second and Third Ages.

: PS: Personally though I never bought the idea of the Dunedain of Cardolan and Rhudaur just disappearing.

:::I never believed either, it has always been my opinion that they fled to Arthedain, as Rhudaur was controlled by wild men, and therefore by Angmar, so the Dunedain there would have fled west (or, as is my opinion, they took refuge at Imladris).
As for Cardolan, being the southernmost province of Arnor, it was devestated most by the Great Plague, and it was also laid waste by Angmar, so I believe that they also fled north. I think it was mostly deserted several years after the Great Plague, as most of the people perished, so they just went north to live with other Dunedain. This is perhaps why the Dunedain's population was so wiped out when Fornost and Annuminas fell, because most all the Dunedain of Arnor gathered near those cities, and when they were sacked, most of the people died.