Preventing Further Abduction During Proceedings: Is it possible that a parent who has abducted children to Israel, could try and abduct them to another country once he/she knows that the other parent is going to take legal proceedings?

Yes, that is why it is wise to apply for an urgent, ex parte order preventing the children from leaving Israel, at the same time as the main Hague Convention plea for their return is filed at the Family Court in Israel. This is usually granted as a matter of course, and a copy of the order immediately sent to the border police.
Abduction To Israel