If we want to be realistic about it—and god forbid a story like this ever ignore the speed limit—then quantum entanglement doesn't allow for FTL communication. What it allows, communication-wise, is a form if quantum cryptography; at the simplest, a variant of a one-time pad encryption where you can be a little more certain no-one ever intercepted the pad.
There'd still be lightspeed lag, though. That's not something you'd notice on earth, but in space is a different matter.
Except the Fog explicitly have quantum communication systems with literally instantaneous transmission times. With "telepathy" a full, complex, concept can be transmitted and understood instantly. I see no reason why this expedition should not have full broadband access to Earth's systems (free TV and e-mail for the crew + political updates, etc.).