That just isn't true. It would be true if there's a particle that moves at infinite speed in one particular frame
, but no tachyons and no particles that move at infinite speed in any other frames, but that's definitely not what the question was about.
If it's possible to send messages at arbitrary speeds (and detect the signals in a short enough time), there will be paradoxes, as I explained in #3. If you google for it, you can probably find a site or an article that explains what I said in #3 with a spacetime diagram, or you can just make one yourself.
Yes, and we can say the same thing about Minkowski space without tachyons. (The universe we live in doesn't have a flat geometry).