Can one parent be awarded compensation by a judge in Israeli family court proceedings if the other parent has been found to have made false accusations of child abuse to get a protection order and manipulatively prevent unsupervised contact with the child?

Yes- but only after there is clear evidence that the parent applying for the protection order and suspension of unsupervised contact was lying and acting in bad faith. For example, in a rare case, the February 2016 Nazareth Family Court ordered a divorced mother of a 4 year old girl, to pay the father (her ex-husband) 15,000 NIS compensation after polygraph testing (to which they had both consented ) showed most clearly that she had made false claims of child abuse, while he had been telling the truth. There was a history of bad faith and manipulative behaviour on the part of the mother, in legal proceedings against the father, and she had tried to cover up results of additional testing ordered, which proved unfavourable to her, it was stated in the judgment.