Barring significant new physics, nothing can travel faster than the speed of light. And that's really a very probably no - although you see popular science stuff written like it can solve the problem, it doesn't, and we have no real expectation that anything will.
Dark matter, if it is matter (and there are good but not totally confirmed reasons to think it is) is just that...matter. It would really be not that special at all, except that it doesn't interact electromagnetically, but this doesn't particularly have deep implications - we already know about particles like that, neutrinos, but they happen to be lighter than the ones that would make up dark matter.
Given that we know very little about gravity and other effects that distort space-time, it's conceivable that faster than light travel may be possible without violating the relativity limit, by distorting space. We don't think that it is possible without producing the ability to travel back in time -- which is considered impossible --, but we also know very little about the subject.
We're nowhere near it, but clearly at the stage of: we know that we know next to nothing about it. Just have a look at the discussion around the Alcubierre Drive and you'll get the feeling that it is pie-in-the-sky science.
So, I'd wager it's not a "very probably no". It's a "we have no clue".
There are lots of interesting questions about what this would really mean, but it wouldn't break the FTL barrier - it's really taking a shorter path, not taking a long path but going faster.
This potentially raises paradoxes etc, and may also be impossible, but it doesn't break the barrier in the above sense.
The universe initially expanded very quickly but not at the speed of light.
A university professor of mine[0] who was (perhaps still is) involved directly in international scientific efforts to examine the expansion of the universe once explained the speed of expansion of the universe to me in a way that made perfect sense.
Unfortunately I can't remember the precise details but the concept relates to a change in scale of the distance between bodies.
My best approximation is this: the measurable distance between two points can increase without either point moving if the nature of what is between the points changes.
You can pseudo-simulate the concept as follows:
1. Open Google maps at a reasonable "normal" scale
2. Affix two dots to your screen and take a guess as to the distance between them as if the dots were actually on the map
3. Zoom out the map quickly as far as it will go
4. Guess again the distance between the dots
The ground distance between the dots increases dramatically. One could argue that the dots moved apart at a great speed, possibly greater than the speed of light if the change in distance is sufficient.
Clearly we know that the dots did not move. The scale of what was between them moved.
During the initial stages of the universe things behaved very oddly.
