I am not Romanian but sort of wanted to help. There are Slovak gypsies, Hungarian gypsies etc. Have you looked in the Ellis Island web site for the name Farrar or Farar just for the informative avenue?
Have you checked out the Romanian phone book for the name? I kind of doubt that you are of Romanian gypsies.At that time it was communist government and they did not allow people to immigrate or emigrate that easily as now.