Is there any other reason to split ISS to Russian and NASA side than pure logical?

Question

While browsing this site, I saw several references to "Russian side of ISS" and several questions arised in my head. The root question is:

Is there any other reason to split ISS to Russian and NASA side than pure logical?

Examples. In normal mission day on ISS (standard procedures, no emergency):

• Can astronaut freely move wherever they want on ISS? (In their free time)
• Do Russian astronaut sleep in Russiann side, while NASA/ESA ones sleep in their side?
• Is "sleepover" allowed? (Russian astronaut sleeping in NASA side. Zero-G pillow fight involved)
• Are there separate Russian/NASA missions or is there only one "common" mission ivolving astronauts from all nationalities?

Edit: By pure logical, I mean, that I am assuming answer: "Russian side of ISS is called Russian simply because Russians did put it up there"

Answer 1

In order:

• Astronauts and cosmonauts can and do move freely between the two segments. It's one crew and one station; it's not a Russian station docked to a US station.
• Crew can sleep in each others' segments. There are two crew quarters on the Russian segment and four on the US segment, and typically three Russian cosmonauts aboard, so there's normally at least one Russian cosmonaut sleeping in USOS. US astronauts used to sleep in Zvezda routinely back when there was a crew of 3 and only the two quarters in Zvezda, but now I think Zvezda is mostly Roscosmos (since the non-Russians can all use Harmony).
• As mentioned, crew can have quarters in each others' segments. I'm not sure what you mean by "sleepovers;" you won't see crew sharing quarters (they're a) not big and b) the only private area on the whole station), but crew could sleep anywhere on the station if needed (you just need a bag to keep yourself from drifting off). However, I don't imagine this is horribly common to do for fun, because you're already living with crewmates -- a sleepover doesn't really add much to that.
• While there are Russian missions, US missions, ESA missions, etc. (each partner can run its own scientific missions), the crew also does a number of joint experiments. If Roscosmos or NASA is running an experiment, it'll likely be their own crew doing it; joint experiments are done jointly. Station maintenance seems to be a joint activity.

The Russian segment and USOS differ in a few ways. For one, there are engineering differences between the two; there are compatibility circuits installed. They generally have different docking/berthing connectors. They have different spacesuits. Different modules are controlled by different agencies. Most of the Russian orbital segment belongs to Roscosmos (Zarya is NASA-owned). So there are differences between the two; it's a useful distinction to make for some purposes. But it's still fundamentally one station.

Answer 2

The Russian side has sleeping spots for three people in Zvevda and the US side has sleeping spots for four in Node 1 (Unity). Usually the Russian crew sleep on the Russian side and the US crew on the US side. (Europeans? They flip coins?)

There is a bathroom on the US side and one on the Russian side.

I do not think they do sleepovers, because the sleeping spaces are not really shared, rather they become the only really personal space for 'your stuff' on the station for each astronaut/cosmonaut.

The Russian side has been described as loud and noisy. The US side, while many fans and stuff going on is apparently much quieter and nicer place to hang out.