as for the checks and balances... the queen is broadly considered a goddess by the general populace... this is enforced and by the state church, the Temple. there are zealots in all levels of society and all walks of life.. much as there are more detached and cynical and even non-religious individuals...
a fair bit of the population are Children of Zeta, children born through the...breeding policies enacted by the Temple.
The Children of Zeta who are not adopted into families, enter the service of the Temple, one way or another, or enter the palace bureacratic apparatus, or the army. This means that all 3 of those institutions are in a solid percentage populated by Children of Zeta, who got most of their basic (and advanced) education from the Temple itself.
The queen is, at least, nominally, above the temple on account of the temple being pretty much dedicated to the cult of the queen, both as an individual and institution.
Of course, there are those, in the Temple and elsewhere, who play a role into selecting the new queen, and raising/educating/shaping her... it stands to reason that at least some of those would be people less enchanted by the supposed divine nature of the queen... then again, the Catholic Pope can be a political nomination but even then, the cardinals all swear by the fact that their votes are guided by prayer and divine inspiration, and the masses of Catholics will still consider the Pope as a divinely guided ultimate authority on all matters religious, if not more.... so there...