If we had some absolute zero reference outside the universe - let's call it a great alien petri dish - we probably could find something moving faster than the speed of light, in reference to that absolute, out-of-universe observation point? But measuring that might be hard.
And on the other hand, we might be able to find two objects which are static with reference to the universe, but actually increasing the distance from each other at a speed beyond c or rather 2c, which should be impossible, because the universe between them expands?
This is very weird to think about, but accepting your reference framework - the universe - changes makes it easier.
Yes. Picture an ant walking on the surface of a balloon. You could conceivably blow up the balloon faster than the ant could walk across it. If you were blowing up an infinitely stretchy balloon with an ant at the far end, you could conceivably blow it up fast enough that the ant could never reach you.