I think that is entirely expected from what we know of modern physics. It doesn't say you can't do it, just things are very weird if you can.
Exactly! It’s not forbidden, just very unlikely and would be very strange.
It’d likely involve exponentially more energy as well. It’d be a good sci-if plot point if FTL communications required machines the size of Jupyter to get a few milliseconds of prescience.
I think it's more likely that modern physics are wrong than that all of those weird things happen. We might simply discover a preferred reference frame, instead.