It's a different situation: before the radio was invented, people had no idea ho to communicate that far, but they no reason to believe it was not possible at all: it was just a matter of technology. Regarding talking in real time to Mars, already a century ago they had good reasons to consider it impossible: the scientific knowledge of the world is (and already was a century ago) incompatible with faster-than-light cause-effect relation.
One thing is not to know how to do something, another is knowing it to be impossible, short of stunning scientific discoveries.
No.
Consider this- There is a lake which is 50 meters wide but 500 km long. You want to cross the lake. You are at the middle of one side of the lake. Now to cross you need to travel aproximately 500km if you follow the bank.
Now if your maximum speed is 6 km per hour yo need more than 80 hours.
Now you get a great idea to create a bridge on the lake- Time to cross is reduced to a minute or so. Now what you are doing is instead of walking one dimension following the bank you just bridged the two places using second dimension.
I do not know if it is possible to create a bridge among two places using another dimension or not- but it is alwaws a possibility and you can do it by travelling less than speed of light.
A wormhole is another possibility, but connecting both ends of an Einstein-Rosen bridge to the same universe would render it too unstable to be used for any sort of communication, as it would collapse before light or radio signals could make it through. One could theoretically get around this by creating two wormholes to a separate universe, with the endpoints here separated by distance and the endpoints in the other universe very close (so that signals/matter/etc. travels to the other universe and back). In effect, this would work similarly to 'hyperspace' in some sci-fi (e.g. Babylon 5's jump gates).
Still, as important as latency is here on planet Earth to the financial trading witch doctors in New York, Tokyo, and London, seems odd no one's been able to monetize this idea as yet.