Okay, just manipulate and measure the velocity then. It seems simple enough, in theory if not necessarily in practice.
As to the other, we would not have a business interest in simple communication across the galaxy at this time, but in getting ourselves back and forth. That is the goal. Make it happen.
I'd love to, to be honest, but I don't see it happening in my lifetime. Developing ansible communication, on the other hand and as has already been pointed out, has any number of applications beyond communicating with one's interstellar starships and colonies: The ultimate in uninterceptible communications, real-time control of our interplanetary missions, etc.
I'm just still unclear on why FTL communications would cause such paradoxes that they must be impossible, as some here claim.
I can't help with that since I don't see a problem either.