Yes the wick inside the chamber is sort of a reservoir, surface tension along with the negative pressure in the tank only allows enough juice into the system as needed to keep it saturated.
When the wick is through those slots you have to be more precise with wicking, too much and you create a choke point, too little and it can run freely into the chamber and cause flooding.
The tails aren't really folded, you just grab the end with your tweezers and sort of push it into the chamber so that the end is against the bottom, and bend at the shoulder is sort of pushed up against the wick slot.
Yes Rayon is pretty economical, I bought three packages of ... cotton Shisedo, Muji, and KGD, I've barely put a dent in it in the couple years I've had it probably another year or two before I need to consider buying more. Have a big baggy of Rayon same thing barely used any of it.
As for the difference, main difference is Cotton expands Rayon does not, many say Rayon lasts longer has less initial taste and or shorter break in period. Not my experience.
I'm sure many factors come into play, down to the individual juice your using. For me time between rewick is about the same. I taste both, neither is a good taste, both go neutral after 5 or 6 pulls.
I don't use cotton balls, just the Japanese cotton pads, I think the main reason I prefer them is simplicity, I just cut a strip off the pad very easy to get consistency, just cut the same width. They are always the same density. Rayon isn't much more difficult, but for me cotton pads have the edge for consistency.
Here are a few more pics of the wicking, this is a Hurricane so pretty much same thing.
