Might a psychologist that the court appoints to give a child therapy later be appointed as the court appointed expert who provides a report in custody proceedings, so the minor does not have to go through more tests, and waste more time before he opens up to somebody new?

This is unlikely due to the emphasis on the separation of treatment from assessment in the code of ethics binding psychologists, though a report made by a psychologist appointed by the court, with the consent of the parents, could become part of the proceedings and he/she could be cross-examined as an expert witness, during custody proceedings. If an application of this kind is to made by one parent during proceedings, the court would most likely request the reaction of the other parent, and the professional, before making a decision.

In November 2017 Nazareth Family Court stressed that a psychologist whom it had appointed, with the consent of the parents, to give therapy to a minor, would be an expert witness, and his report part of  custody proceedings. It did so after a request by the father, represented by our offices, to broaden his appointment, or allow him to give testimony as an expert witness.