Saved is everything that is submitted. I use group by group mode. If I leave a page without hitting the next button, the answers of that page are not saved.
I recommend that you try it on your own with a short demo survey.
Different people working on different sections of the same survey is always tricky, in my opinion. I personally would probably rather provide the company with 1 survey per section, then to risk that 2-3 people have to fill in the same survey. Via the token you can still connect the different responses of the same company.
Help us to help you!
Provide your LS version and where it is installed (own server, uni/employer, SaaS hosting, etc.).
Always provide a LSS file (not LSQ or LSG).
Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.