There are definitely Paladins of Auri-El. I don't see why there can't be some Imperial version of those somewhere.

I suppose some of them do worship Talos, but is worshipping Talos required to become a Blade? I suspect that no.

Well... Talos is a god version of the being they're supposed to be serving. As soon as the Blades find another Dragonborn in Skyrim, they begin serving it instead of the Mede line.

Serving a Dragonborn means more than serving an Emperor. It just so happened those two roles coincided for centuries. I think Talos worship is practically guaranteed.

Melissa Raven, the Dunmer Member of the Blades, Serves under my Take of the Dragonborn. she is ok to kill Dragons but she will not allow the Dragonborn the attack Paarthurnax since he turned a new leaf.

I am going to leave this here.

And what if a Blade is, let's say, a Khajiit? Or even an Altmer? A guy who loves the Empire and all such, but doesn't worship Talos?

Is there a specific organization within the Empire tasked with gathering intelligence?

The Penitus Oculatus, a.k.a the Blades' replacement, does that.

Anyone know of 'modern' lore involving centaurs in Elder Scrolls? Their last appearance was way back in TESII: Daggerfall (though if the 3D skeleton files are an indication, they were considered for inclusion in Skyrim). Anyone know anything about them?

As Ian says, Penitus Oculatus. They not only serve as Emperor´s bodyguards, but also as spies, assassins and many other things. Both TES Novels do a pretty good job with portraying them, because of one of the main characters, Colin, is Inspector of Penitus Oculatus.

Penitus Oculatus means "The Inner Eyes" or "Inwardly having Eyes" or "“having thorough eyes inside,”

They are mostly known as inspectors, but sometimes reffered to as "spectres"

Both The Rise and Fall of the Blades and A Concise Account of the Great War Between the Empire and the Aldme... have some info on them, but most of the info comes from Infernal City and Lord of Souls.

If you´d like I could dig something. Just say what you are looking for.

Sadly, no. While they appeared in Daggerfall there is no recorded source about them, so I´m afraid I can´t help you here.