There are mods that do quite a few of the things you want, but not all. To go down the list:
Religions: There are a couple mods that add religion-like systems to the game, but they're not generally the Civ4 style. A previous poster mentioned Echoes of Ages, and my own Mythology mod (see .sig) uses its own religion system, but it's not a very Civ4-ish one at all.
Corporations: Since the corporations in Civ4 were basically just religions by a different name, it's the same answer as above.
Espionage: Not really. Some mods have espionage (again, like my own), but it's usually a very non-interactive wonder-based system that either depends heavily on random chance or just weights other things through Lua. For instance, Thalassicus' "Vanilla Enhanced Modpack" changes the benefits of a Research Agreement such that the tech leader gets less and people further behind get more. Or there was a Tech Diffusion mod that'd give each player extra beakers when they'd research a tech that other players had already finished. These have the same basic effect as espionage, but they're not the sort of active spy-based systems of earlier games.
Realistically speaking, to have the kind of espionage systems most people want, we'll need the DLL because otherwise the AI will never be able to handle it.
Random Events: Back when Civ5 was still pretty new, a modder named veyDer created the template for a good random event system, and
this thread includes a mod that tries to use that system to add a nice set of events for other people to use. However, the version in that thread has one major drawback: the decision process only applies to the human player, not the AI. (The EFFECTS can apply to any number of players, but you can't offer the AI the same choices the human gets and allow him to pick a different outcome.)
My own Mythology mod, at present, is the only working version of the user event system that DOES work for the AI. I've been trying to help the folks in that thread implement the fix into their version, so in the near future you'd be able to use theirs, but it's not there yet.
The bottom line is that if you want a game that plays very differently from vanilla Civ5, you won't find any mods that do this, because modifying the AI behavior in any significant way requires the DLL, which we don't have access to yet. You can still download some good mods that heavily alter the gameplay, but you're not going to get a pure Civ4 conversion any time soon (if ever).
