This presents several challenges to designing the setting and plot of my (admittedly theoretical) game. I'd have to figure out how an interstellar society with time travel would work.

Heavy regulations.

It realy depends on how easy time travel would be, but i 'd expect that ID-chips would have an internal clock that can be checked just to make sure that people/authorities know it when dealing with someone from the future.(and all kinds of creative ways to get hack the system)

Maybe special forcefields that prevent someone from another time to enter the time-place of that forcefield.

Getting help from the future would be an option as well, when you need help you just decide to ask/find help in the future and sending it back.

Most FTL is accomplished by moving space, not matter. Space can move as fast as you like as far as we know. The universe expands at something like 3 times faster than the speed of light. That's how they do it in star trek. They move the space around the ship to move the ship instead of directly moving the ship. Since the matter isn't moving at FTL speeds, infact it's not actually moving at all, it's time remains constant from when it left.

It's like putting something in a box to move it. The thing itself isn't moving, but the space containing the thing is moving, so it moves the thing along with it.