The Crystal Empire

The status of the Crystal Empire following the Great Cataclysm

Following the Great Cataclysm, Twilight, Luna and Celestia disappeared. Cadence turned the Crystal Empire into a running democracy in order to ensure its safety before she and Flurry Heart left to seek the other allicorns, never to be seen again. 
Ever since she left, the Crystal Empire has been run by a council similar to Ancient Greek democracy, which over time has descended into corruption. 

Nowadays, the head of the Crystal Council is probably the most well connected person in the post-cataclysmic world. He is one of the few that knows of the Frozen Empire and the Knowledge Treaty. He actually met the one who is at the top of the Frozen Empire's council, the one that no grifix knows who it is. He also prides himself with having Sunburst, one of the Crystal Empire Protectors as his ancestor.

The greed of the council is probably the reason why the Crystal Empire has not joined the Knowledge Treaty. They refuse to surrender their knowledge and will often use artifacts and manuscripts as leverage to obtain certain things from factions involved in the Knowledge Treaty.

The fueling of the Crystal Heart in Post-Cataclysmic Crystal Empire

Over the 2000 years the Empire's council members became corrupt, and the spirits of the crystal ponies started to die out. The Crystal Heart started to lose its power, until the council came out with a symbolic “princess” in order to lift the population’s spirits. 
She is nothing but a puppet in the hooves of the council but she is like an idol to the people. She is the “Crystal Princess”, the same title that Cadance and Amore wore. And the council claims that she is, in fact, their direct descendant, as absurd as that is now, 2000 years after they left. She is disguised as an allicorn with magic, but she is a mere unicorn, without any more power than others.

She is used by the council to influence the crystal ponies, lift their spirits and manipulate public opinion. Their love for her and joy keeps the Crystal Heart beating and alive. 

There have been many Crystal Princesses over time, for they are not immortal. The old ones warn the new of how they will be used and manipulated… yet none of them seem to be strong enough to change everything. After all… changing might mean losing the protection of the Crystal Heart. And nobody would want that…
That's how they blackmail her into doing anything the council wants, by telling her that if she doesn't they'll tell the crystal ponies, which will make them hate her for lying, crush their spirits, and the Empire will fall.

The Church of Time in Post-Cataclysmic Crystal Empire

The Church of Time as an institution has been completely wiped out in the events surrounding the capture of their god, Akasha, and the birth of the Two Alicorn Sisters (Celestia and Luna). It only existed in story and sporadic worshippers for as long as the alicorns reigned over Equestria. For the ponies of Equestria, it became an ancient religion, no longer practiced.

Following the fall of Equestria caused by the Great Cataclysm, the Church of Time has been brought back as a rather exclusive cult that slowly started to fill in the gap left by the alicorns. They're not a public church but they secretly influence most of everything that's happening in the remaining pony settlements in Equestria, especially in the North, they fail to have much influence in the remote settlements of the Wild South. They do, however, have strong connections everywhere.

A great number of the Crystal Council members are part of the Time Cult, and the head of the Crystal Council is actually the great priest for the Cult of Time.

The crystal academy

The Crystal Empire is a university center in Equestria and contains records of knowledge that has been saved from before the Great Cataclysm.

The university from the Crystal Empire is called the Crystal Academy, and its libraries hold almost all the world's knowledge between their walls. It is only, perhaps, the Frozen Empire's library that hold more knowledge than this.

The Crystal Academy also regulates most of the trades in the Empire, including the trades with the Frozen Empire.