I don't mean to be a downer, since some of the ideas proposed are great for the image of an insane and decadent monarch, but they raise at least two questions:
1. Where is the magic for all of this coming from? In DnD 3.5, for example, while turning convicts into statues sounds cool... but the rationale is that it's easier than sculpting... which is untrue because there are lower level (ie, more plentiful) spells that do the exact same thing. Flesh to Stone is a 6th level sorcerer/wizard spell. Fabricate is a 5th level sorcerer/wizard spell. Stone Shape is a 4th level sorcerer/wizard spell.
Sure, you have to get rock there, but it's easier to get rock and magically turn it into a statue than using tons 6th level spell slots per day.
(Note: This problem can be resolved by having a Gorgon, such as Medusa, working for you. Other examples of this problem are not necessarily so easily resolved.)
2. If there are people powerful enough to execute these insane projects, how come they haven't disposed of the monarch, either though assassination or mind control? My experience is limited to DnD, so please bear with me, but if I was a spellcaster capable of casting enough 6th level spells to turn a sizeable portion of the criminal population into statues, rending an inbred aristocrat inert would be a piece of cake.
I am aware that other gaming systems are not like DnD, but I feel the points may come up in them as well.
A couple of things:
Fabricate and stone shape still requires you to make an appropriate craft check. The most life-like statue will be one of a live person. Not many mages seeking power or prestige focus on Craft: Sculpting.
Between charming monsters with stoning abilities and metamagics which increase the number of targets of a spell, and perhaps even alchemical creations - you can speed up the process to meet the emperor's nearly impossible demands. This is not to say that thousands of sculptors aren't used as well - but if mages across the empire engage in a systematic stoning of unwanted population - they might actually meet this month's quota.
Also, just because the emperor is a potentially inbred, decadent, dissociative incompetent doesn't mean he isn't protected. From what little backstory PCat has shared, many many many prior emperors were capable, and most likely magically astute.
The current emperor probably controls multiple powerful magic items, or even artifacts, that are tied to his bloodline or rightful position. Hell, the capital city or imperial palace might BE an artifact. Great magics from a bygone age likely limit the ability of assassins and attackers to easily kill him. And similar magic items are likely required for mages in service to him, which equate to a geas or similar, which causes even these powerful servants to accede to his whims.
That doesn't mean they can't manipulate him with words and actions. Either they can be a power behind the throne, or they perform the ludicrously expensive demands of the emperor, while intermediaries work to find how they can lawfully depose him to become the emperor themselves, or at least find the loopholes in the various methods set in place to protect his august presence.
So, if the GM asks for projects that literally shoot for the moon, then you shoot for the moon! (We are, after all, just giving ideas, he can mold them as appropriate to the amount of magic/expense he sees fit for his world)