No - there's nothing stopping you from using an Al stem with a carbon bar - just be mindful of the appropriate torque on the clamp bolts.
Also pretty sure that any number of integrated cockpits will accommodate wired electronic transmissions (I'm making the distinction between "wireless" as you used it and "electronic"). You might have trouble getting a mechanical (Cable-op) transmission to work with an integrated cockpit, but electronic (wired or wireless) shouldn't be a disqualifier - but I could be wrong, I'm a bit of a Luddite.