Is the will written by the father, which stipulates the transfer of his properties into an endowment (waqf) for his sons and daughters, with details concerning the entitlements of sons and grandchildren, considered valid and enforceable, especially since it was not signed by all heirs, nor does it bear the signature of the father or witnesses, but only the signature of the judge? And can it be challenged?

It is permissible to make an endowment for one's descendants, such as children and their offspring. If one endows for his children, the children of daughters are not included unless explicitly stated. So, if he says: "This is an endowment for my children," it will be for his male and female children equally, then for the children of his sons, but not their daughters. This is because the children of daughters are not included in the term "children" in the Holy Quran, nor in common usage and language. This applies if the endower uses the expression generally, but if he explicitly states their exclusion, the matter becomes even clearer. The aforementioned endowment is valid, and if approved by the judge, there is no issue with it.