FTL communications pretty much has to exist unless you want to run a single solar system and have status reports that are years, decades or centuries old when they arrive.
It'd be an interesting game, but it's not the genre Stellaris belongs to.
Edit: Actually, thinking about it, Paradox have been quite selective and cunning with their "FTL".
Warp drives as proposed move space, not the ship, and don't actually break the rules or accelerate the ship.
Wormholes just connect two points in space and the ships move through normally.
Hyperspace has the ship move outside the normal universe and return, further away.
None of them would cause time dilation effects. Ironically, that's really a STL issue...
As far as communication goes... well, if you can get a ship there, you can probably get a small robot courier there, possibly faster than a ship. Wormhole stations would be able to swap intel with any system in range just by opening a small wormhole for the purpose. Once the courier hits the target system they can laser or radio the data and head back. It's also conceivable that wormholes could be directly modulated as a means of communication, though the courier trick would probably be more efficient and give bettter data density.
I think so as well, since Paradox likes to simulate things very accurately, so if they don't want to deal with transmission lag, it would be useful to have FTl techs that bypass the light speed limit via some kind of trick. But I think courtiers are somewhat more secure than beaming data out, since anyone can manufacture or intercept it if they knew where it came from.
The courier could even be a cyborg and have a lot of SSD drives installed on em, encrypted using various stuff.
For normal non classified information, trade vessels would probably be the go to method, which would make it similar to some frontier towns using horses. Well, that would be that "information control" edict that limits ethics divergence then. Better than the CK2 method of teleporting generals into the Holy Land to get Crusader, at least.
EDItted in:
(Disclaimer: I really have no idea what I am talking about)
Quick question, why does Stellaris (and other Space Games I assume) all have FTL travel when it is physically impossible to exceed the speed of light* and getting close to light speed is plenty fast enough anyway?
* or so I have been told...
EDIT:
My question has been answered, thanks!
They use tricks and shortcuts, sort of like how time travel theories work with wormholes and exotic matter.
If you are interested in the latest effective FTL theories, check up on the Mexican physicist, Alcubierre and his drive. Mathematically, it requires the use of exotic matter or in this case, the Casimir effect, various quantum states that can achieve the same effect as exotic matter, except done through the Standard Model of quantum physics.