After reading that time stops at the speed of light and at event horizons I wondered if when the speed of light is exceeded does time loop backwards ...
The thought struck me too that the term space-expansion might also imply the space between subatomic particles ...
Answer
The question you ask isn't well-posed (whose time is "flowing backwards?") but there's still a clear answer: no.
This is because the expansion of space is unconstrained by the speed of light. No physical thing can travel faster than light, but the universe can still expand faster than light because it's not physical. Since the expansion of the universe isn't physical, we can also say that the usual special relativity effects such as time dilation don't apply.
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