Wonderfully written overview — not easy to do for a non-scientist. Congrats on that.

Time did not go backwards in the experiment. However, it has been shown that a quantum mechanical observation can influence and event that was earlier in time — thus, time can go backwards in a sense, but not in the described experiment.

Regarding many worlds, all that is required is that each observer have their own reality. There need not be an infinite number of realities. But if each observer has their own reality, then the Copenhagen interpretation is true — the observer is indeed central to things somehow.

The case is not closed at all. People are still trying to make sense of the matter. The original paper is here.