The introduction of FTL travel/communication in a relativistic universe may effectively be equal to having a time-machine with all the problems that may entail for causality.
I would like to avoid that in my setting and I think I have managed. But I'm not a 100% sure of that. So please, look at my setup and tell me if I got it right or wrong.
The non-FTL bits:
Ships can do up to 0.35C and accelerating to such speeds from 0 takes about 24 hours. There is some handwaving technology like "artificial gravity" and "acceleration compensators" to keep the people inside the ships comfortable.
All inhabited star-systems make use of "Terran Standard Time" which is a sort of NTP system on steroids that provides a single consistent time-source everywhere. It makes use of signals from pulsars and quasars to synchronize across star-systems. Local clocks and clocks on-board ships that are subject to time-dilation can be calibrated against this time-system.
This also provides an "independent frame of reference" which is often important in discussing relativistic speeds and FTL.
The FTL part:
Ships go FTL by means of a Hyper-drive. This drive makes jumps varying between 0.5 and 10 light-years. (The maximum/minimum distances are determined by several technical limitations of the drive.)
After a jump the Hyper-drive needs to cool down and requires some re-calibration. This takes between 1 and 2 hours depending on the exact type of ship.
You can't install 2 drives and use them in turns to minimize the down-time between jumps. (You can't even have a spare drive as cargo.) The unused drive will resonate with the active one and the result is spectacular, but unfortunately such a mini-supernova is rather fatal for anything within several light-seconds.
Furthermore Hyper-drives are sensitive to gravity. You can't start a jump or end one too deep inside the gravity well of a large mass like a star or a planet. If you try anyway you will cause the same mini-supernova as you would get by having 2 drives on-board.
This unsafe zone is called the gravity shadow and for our Sun the gravity shadow has a radius of 3.5 light-days. For a star 4x as massive the radius is 2x as large. For most planets the shadow normally falls within the much larger shadow of its star (e.g Jupiter has a shadow just over 2.5 light-hours) so you normally just ignore the planets.
It makes no sense for a FTL ship to travel for weeks inside the shadow to deliver the groceries to an inner world, while meanwhile it could have traveled to several other star-systems. So FTL ships typically stay clear of the shadow altogether and will transfer cargo and passengers to in-system ships for further distribution.
The ship must travel at a minimum velocity of 0.23C before a jump can be initiated. When the Hyper-drive kicks in the ship simply vanishes from normal space and re-appears some time later at the endpoint of the jump. The ship will exit the jump traveling at the same velocity and in the same direction as before the jump started.
For an outside observer the ship will have covered the distance in jump with an apparent speed of approximately 2 light-years per hour.
The people on board will notice nothing strange except that the view out of the windows will go completely black. Time progresses normally for the people on board at the same rate as it as doing before and after the jump. So for them the time in-jump will be slightly less than for the outside observer due to the time-dilation in effect when the jump was initiated while traveling at a minimum of 0.23C.
(Why this happens is a question that has been driving the astrophysicists nuts for centuries ever since the FTL drive was discovered. Every theory insists that on-board the jump would appear to be instantaneous, but that is just not the case.)
Ships in-jump are completely isolated from normal space and each other if they happen to be in-jump simultaneously.
There is no FTL communication in my setup. Communication relays throughout a star-system forward messages to FTL ships about to leave the system. The ships will offload these messages to the comms-relays in the destination systems upon arrival.
For routes where there is a lot of communication traffic small drone-ships jump back and forth at regular intervals just to carry messages. These drones are called "ponies" after the Pony Express.
These "ponies" are also used to get a replacement Hyper-drive to a ship with a broken drive. After all, due to the resonance effect, you can't transport a spare drive on a FTL ship. So a pony is send to the ship and the ship's engineering staff will remove its drive and put it in their own ship.
That was a long story but I wanted to give you a good feel for the setup.
Now for the big question: Is there some way to exploit this setup for time-machine shenanigans?