How much were Bartok's melodies his own and how much were they copied from/based on Romanian folk melodies with his own harmonies?
I'm thinking especially of his pieces like Romanian Folk Dances and Romanian Dances, but also am interested in his melodies for other works.

Gilels plays Romanian Folk Dance:
http://www.youtube.com/watch?v=BnIdLGiqrc8&feature=related

Bartok plays his Romanian Dance No.1:
http://www.youtube.com/watch?v=ibaWiMYYUnw&feature=related

Were Bartok's Romanian Folk Dances and Romanian Dances based on folk/national melodies the same way Liszt's Hungarian Rhapsodies(I think?)were?

Is there a special scale that Bartok tends to use in his music that gives his melodies their special character?

Some of them were folk melodies. Others were original. Sometimes the scores say so. Bartok's recordings of folk music are available. You can go through them and see where he used them.

Interesting question. Undoubably all composers reference from sounds they hear. Someone as "complex" as Bartok is difficult to judge. Fritz Kreisler, the violinist is argued to have "made up" several of his reference points.

Here's a fascinating program note on the "6 Romanian Dances" and "Sonatina":

http://www.fuguemasters.com/bartok.html#Dances_Sonatina

According to this writer, all of the tunes in these two pieces are folk tunes, and he tells us exactly where they are from and how they were danced.