Thank you.
A. Is the claim that it would have been proper to intercalate the year correct?
B. Does the prior fixing of the calendar block the possibility of intercalation when needed? Would that distort the calculation of future years?
B. Is the Chief Rabbinate unable to intercalate the year because it lacks legitimacy or motivation, or because it lacks authority? Is there any other body with the authority to intercalate?

Strictly speaking, nobody today has the authority to intercalate years. The calendar is fixed. Still, there is room for the reasoning that if all the sages of the Land of Israel were to agree, they could do so. Certainly according to Maimonides, since in such a situation ordination can be renewed, but even according to the other views, with full consensus it would be possible to enact an emergency ordinance (in the third book I called this a freeze, and I showed this from Maimonides’ wording in the Laws of Rebels).
In any case, the Chief Rabbinate has nothing whatsoever to do with any of this. It is a secular governmental institution and does not possess a shred of rabbinic authority. Therefore, a petition demanding that the Chief Rabbinate do something like this is ridiculous. It does not depend on it but on us (that is, on whom authority is granted to act on behalf of the consensus, if such a consensus indeed exists).
And in general, it seems bizarre to me to petition the High Court of Justice on a religious matter. The High Court can determine what counts as Passover from the standpoint of the law, not from the standpoint of Jewish law. Just as a petition against the Rabbinate in matters of marriage and divorce has no halakhic or religious significance. It has legal significance. The Chief Rabbinate is a government office that can determine things from the standpoint of the law. It has nothing to say on matters of Jewish law. And that is so even if great Torah scholars were sitting there—which is not what really happens in practice.