It's physically impossible to travel greater than the speed of light. In game, the warp drive/alcubierre drive warps space so that while your spacecraft is technically motionless in Einsteinian/Newtonian physical terms, the space between your destination and you is bent so that your "speed", or rather rate of decrease of distance between you and your destination, can be greater than c. Also, this is in play when you frame shift at less than the speed of light, no time dilation. Then there are black holes, and spending time near high gravity objects like stars, which I'm assuming that the warp bubble also negates dilation here (which is why there is noticeable strain on the maneuverability of your ship near multi-solar mass objects). The only real plot hole in the game is when you drop out of frame shift near such an object - then you would experience dilation the degree to which depends on your distance and the magnitude of gravitational field.
You'll notice that your thrusters are off unless you're out of frame shift, so it's not traditional motion. There's also a universal clock in every spaceport you dock at that is shared with everyone else that is always constant with everyone else.
The universe expanding faster than c is simply your frame shift drive, except on a extreme scale - the fabric of space stretching. Also, if you are in a car that goes 90 kph in one direction, and someone else goes in a car 90 kph in the opposite direction, you are moving 180 kph relative to the other guy without going 180 kph relative to your last position. In more complex terms, think of stretching space as an infinitely expanding balloon in which the velocity between any point on the balloon and its previous location cannot exceed c. But this also means the two points on the opposite sides of the balloon will have velocities of 1.9999999....c maximum relative to each other. And even then, these two examples aren't perfect, as stretching space can't be directly equated with motion as we know it.
As for "gravity propogating faster than c", all matter has been present, more or less, since the beginning of the universe, and its gravity has too. The gravitational field of your body/random molecule of oceanwater/Earth/Milky Way/any collection of matter in the universe extends to the boundaries of the visible universe and beyond, except its influence billions of ly away on the other side of the universe is so weak there as to be negligible. This is disregarding the extremely minute portion of matter that has been converted into energy by stars/black holes, atomic bombs, the A class reactor on your Anaconda etc. a la e=mc^2, as well as hawking radiation releasing parts of a black hole's mass. And actually even energy has gravity, so the universe's total gravitational field has been pretty constant since the beginning of time.