Questions worth considering beforehand, just so that you don't have to rule on them ad hoc in the moment:

Over the years I've hit all of these. My own rulings:

How does a fast-flowing current affect the wearer? Do they move along the surface like it's a conveyor belt, or remain stationary aside from their own movement?

The current carries the wearer, just as if it was a moving floor. And see below...

What happens if someone is knocked prone while walking on water? Do they fall in if their feet are out from under them, or do they lie on the surface?

Lie on the surface. But, that said...

If they're already underwater, is there an easy way to go from swimming to walking once they break the surface?

They can't break the surface. In effect it's like ice that way; they're trapped beneath until the ring is removed.

The hard one comes when they remove the ring and are then swimming at the surface. If they don the ring at that point there's several things that might happen:

  • the water surface acts like broken ice that the wearer can, if lucky and-or dextrous, crawl up on to
  • the water surface "hardens" right up to the wearer on all sides, effectively trapping the wearer in place
  • the water surface hardens and eventually, as the wearer struggles, chops the wearer in two

I've never had to make this decision; as whenever I've informed a player that donning the ring in this situation might be a bad idea the player has invariably gone to a plan B of some sort.

How do things like strong waves or choppy, stormy seas affect movement and remaining standing? Is it effectively like walking during an earthquake?

It makes movement difficult, or impossible, or outright dangerous, depending on the wave action.

If a person falls into water involuntarily, such as falling into a trap or off a bridge, how voluntary or involuntary is the water walking? Do they automatically land on it like a solid surface, or do they need to deliberately activate the effect?

It's always-on, so it'd be like falling onto solid ice.

One question that follows on from the first one above: What happens if a current carries someone into a whirlpool or over a significant waterfall? Well, let's just say the end result would be both messy and very, very permanent... :)