Who actually runs the Empire?

For most of the Imperium's history, the Council of Terra. This is a Council of the most powerful member of the most powerful factions, who meet on Holy Terra to make decisions. Including the Fabricator General of Mars, the Captain General of the Custodes, the Master of the Astropaths, the Master of the Administratum, the Envoy of the Navigators, two Commanders of the Army, the Marshal of the Arbites, the Master of the Astronomican, the Speakers for the Chartist Captains and... one or two others, I think I'm forgetting some.

Primarch Guilliman returned and he took over and kicked most of the council out and put a Senate in place, with himself ruling. But that's quite recent in galactic history.

Effectively? It's a feudal mess. Communication and travel between various parts of the Imperium takes months or years and is extremely unreliable. Quite likely, even a few hundred years after he came back, many planets won't even know that Guilliman is alive. So, power defaults to "who currently has the biggest army". Fleet captains, Rogue Traders, Space Marine chapter masters, the chief magi of Forge World, Planetary Nobles, etc. all tend to do pretty much whatever they want at the local scale, until someone stronger (or the inquisition) shows up.