"Space itself expanding" is just a term made up to explain these things to normal people in popular articles. There's no such thing as "space itself", what they really mean is "the coordinate system we happen to be using to describe things in an efficient way that's easy for us to use".
Define space time coordinates according to Special Relativity, relative to our position and assuming a constant speed of light, and you end up with a perfectly valid model of the universe in which nothing goes faster than light, all the laws of nature work correctly, but everything looks really distorted because of Lorentz contraction. The further away you "look" (in a mathematical model, not having to wait for light to get here), the faster things are flying away from us and the slower local time is therefore going. At a large distance away from us, the age of the universe multiplied by the speed of light, things are flying away at the speed of light (but never faster), are infinitely Lorentz-contracted, and are frozen in time. Over there, the big bang is still beginning right now.
Even though this model is a perfectly valid and correct way to describe our universe, cosmologists don't like it very much. They prefer a different kind of coordinates in which the speed of light is the same everywhere relative to the local expanding universe, not relative to us. General Relativity allows you to do this easily, it's just a matter of putting different labels (coordinates) on things. Same universe, different labels for distance and time, like using a ruler that looks normal in the middle but has marks closer and closer together as you move from the center. In that model (which is still the same universe), things look roughly the same everywhere, without Lorentz contraction (except for local speeds relative to local space, of course) and the universe is truly infinite. Things now do fly away from us faster than light, simply because we are measuring their speed differently (with a distorted ruler).
That's what "space itself" really means. It's all just about the coordinates which we happen to choose. It's not some kind of background aether or anything like that. At least, as far as we know so far.
So in the early universe, things may very well have gone faster than light depending on what kind of coordinate system you're using to describe it. Either it was slower than light but distorted because of the enormous amount of energy and high speeds involved, or it was going faster than light and looked differently and far more easy to describe mathematically. Nature doesn't really care.
