Yes. The farthest parts of the observable Universe are getting away from us, faster than the speed of light. The Wikipedia article on "metric expansion of space" can give you more information.
In fact, distant parts of the Universe are moving away from us faster than the speed of light.
Light travels faster (up to the speed of light) in a vacuum, which is empty space. Light travels slower through a medium (matter).
The theory of general relativity does indeed allow for faster than light "travel". Not by accelerating to an actual speed that is greater than that of light, but in terms of squishing space in front of you and expanding space behind you, using enormous amounts of energy. There are galaxies, so far away that we cannot see them, that is speeding away from us faster than the speed of light because the space between it and us is expanding. If alien ships can do this, well - it is the same as asking if there are aliens in the first place. We don't know.
Some of the furthest galaxies are believed to be "travelling" faster than the speed of light. They are not actually "travelling" faster than the speed of light, but creating space, faster than the speed of light.
This is an unanswerable question, since time is a dimension and the speed of light a measurement. The two are directly related, however, insofar as approaching the speed of light inversely affects the relative speed with which you travel through time. For instance, one year on a spaceship going 99% the speed of light (it is impossible to reach the speed of light relative to local space-time, in that paradoxical scenario time would stop completely) would cause you to return to an Earth that has aged hundreds or possibly thousands of years (I'm not sure the precise speed to time conversion formula).
The universe is expanding at a faster rate than the speed of light.
It is not. Nothing that we are aware of moves faster than light.
Yes. The farthest known galaxies move away from us faster than the speed of light. While this is not possible for nearby objects, in this case space itself is expanding.
That means that this "horizon" is receding faster than the speed of light from us. In Special Relativity, moving faster than the speed of light is not possible, but in general relativity, it is possible under certain circumstances. "Locally", nothing can move faster than the speed of light - in this case, informally, it is "space itself that is expanding".
we would be all screwed
Usually, in most substances the speed of light is slower than in empty space.
The diameter must be expressed in a unit of distance/length - for example in light-years - NOT in years. The answer is that the distant parts of the Universe are going away from us, faster than the speed of light. Inside its own local space, nothing can move faster than the speed of light. But in the case of the expansion of the Universe, you might say that space itself is expanding. This makes it possible for objects to move away from us faster than light.
The farthest known galaxies / quasars are at a distance of over 40 billion light-years, and are moving away from us faster than the speed of light. Locally, nothing can go faster than the speed of light, and in their "own space", they don't. But in this case, it is "space itself" that is expanding. The Wikipedia article on "metric expansion of the Universe" gives a more detailed explanation on this topic.
No. Speed of light is constant in all frames of reference, even if you are also traveling at the speed of light, the photon will speed away from you at the speed of light. When you see an object, what is happening is that photons are reflected off the object you are looking at and bounce back into your eye. However, if you are traveling faster than the speed of light, the photons can never reach you to start with, hence, you are invisible until your speed decreases to something below the speed of light. It is possible to travel faster than light in many ways. First, if you have a negative amount of energy, you will always travel faster than a speed of light. Another possible way is to compress the space in front of you, then move to your destination before re-expanding the space you have just past.
The farthest parts of the observable Universe are getting away from us at several times the speed of light. LOCALLY, the objects (like galaxies) move at speeds below the speed of light, but in this case, it is space itself that is expanding, faster than the speed of light.
In fact, distant parts of the Universe are moving away from us faster than the speed of light.
the far away galaxies may be moving faster than the speed of light already. In general relativity theory, expansion of space is not limited to the speed of light as it is in special relativity