Do the family have the right to demand compensation from the state for a plot of land it seized more than twenty years ago, allocating part of it for a school and another part for a street? And do they have the right to prevent owners of adjacent lands, who bought their lands based on this street, from opening gates onto it?

If the land is owned by you and its owners or their heirs have not relinquished it, and their silence regarding the state's disposal of it was due to fear and coercion, not consent, then you have the right to demand fair compensation for its expropriation, and your right to it does not lapse with time. You also have the right to prevent the opening of doors onto it until compensation is made, because it is an unlawful disposal of your property. However, it is not advisable to prevent it to avoid problems; it is better to refer the matter to the judiciary or to be patient.