For example, if a light ray was emitted each second billions of years ago, by now we observe that a redder light is emitted every 5 seconds. Because while it was travelling, the space through which it travelled expanded.
When the article says things like "time was slower in the past" it makes my head hurt. Don't they mean "events in the past appear to run 5 times slower when observed today?"
My understanding is that this is dependent on hubble's law, and we do not know the exact rate of expansion now or in the past, but stating an object is 13+ billion years old without that knowledge seems... Unscientific.
Yes, there is uncertainty about the rate of expansion, with different techniques disagreeing. So none of this is fully settled. Which is very scientific!
The separation of event and observer can be mostly in space when observing a relatively close object falling into a black hole, but can also be in both space and time when looking far into the universe (and thus back in time).
It is not due to differences in gravitational fields or relative speeds approaching the speed of light.