Does the colour of the olive oil say anything about its quality?
There are two main factors in quality of olive oil: the flavor, and the free fatty acid content. (Those are fatty acid molecules that are not bound up into oil molecules; they make the oil more unstable, prone to going bad faster.)

Neither of these has anything to do with color, which is provided by chlorophyll and carotenoids. The only exception is refined ("pure") olive oil, which is generally made from oil that already has higher amounts of free fatty acids; it's purified to remove those, and in the process the desirable aromatic molecules are also removed, so it loses flavor. This process would also tend to remove color. But as long as you're looking at unrefined (virgin or extra virgin) oil, that's not relevant.

I suspect time after harvest is not critical, but could potentially make a difference. The olives do need to be at the right point in ripening - underripe olives make bitter oil, and overripe ones make oil with less flavor. So if olives are left for too long after harvest before oil extraction, they could lose flavor from further ripening. Additionally, the flavors come from reactions between fatty acids and enzymes which are released during grinding and crushing, so I suppose this could take place much more slowly over time, especially if the olives have been damaged, and the aromatics produced at that point would be partially lost to the air. All of this said, presumably high-quality olive oils are produced correctly, whether or not they advertise details of the production. The labeling you've seen may just be marketing.

In any case, the surest way to discern quality is direct observation, so just try to find what you like! It probably won't be correlated with color, or any details of the labels.