I read the answer here about large eruvs and how islands and places surrounded by water are the simpler case, and it made me want to understand the whole sugya from the ground up.

1. The gemara in Shabbos (6b) and Eruvin (6a) talks about reshus harabim. Rashi says a real reshus harabim needs 600000 people passing through every day, like the camp of Yisrael in the midbar. Where does that number actually come from, since the Ramban and other Rishonim ask on Rashi that they find no source for it in Chazal? And the Rambam in Hilchos Eruvin perek 1 defines reshus harabim without ever mentioning 600000, and the Shulchan Aruch (OC 345:7) brings the 600000 only as a yesh omrim. So whose shita do we hold like, and how much can a city eruv rely on it?

2. If an island is surrounded by water on every side, isn’t the water itself a wall? Meaning is the whole island automatically one enclosed reshus hayachid, or does it still need an eruv of lines and posts around it? Same question for any city completely surrounded by water or a wall, like the gemara says about Yerushalayim that if its gates were not locked at night it would be a reshus harabim.

3. The part I understand least is the line. A wire on poles is not a wall, you can walk right under it. How does a tzuras hapesach turn a huge open area into a private place? And it sounds like in a real Torah reshus harabim even that does not help and you need actual doors that close, so what exactly is the line accomplishing?

4. So practically, what is an eruv actually doing? Is it changing the area from a karmelis into a reshus hayachid, or is the main part the eruv food joining everyone’s houses into one domain? What is the bottom line halacha for carrying today in a place that has no 600000?