1. Yes, "fix broken links" in the auto import section is the place to change this behavior. I recommend setting it to "No", but others might say that "protect files on missing drives" is better.
2. As you have noticed, it's the act of running auto import that causes MC to remove these files. As I recall, MC runs auto import on startup, and then monitors the disk for changes. When it sees changes, it runs it again. But, if it can't see changes, then it just runs auto import every 1 or 2 hours (I can't remember the timing). If you turn off "run auto import in the background", it should never run unless you explicitly tell it it. This is what I do as it gives me full control. I made this decision after over a year of running "auto import in background".
3. I don't use a NAS. But I'll give you my answer to your "best way to refer to network share" question. In my opinion the best way is with a drive letter. This gives you the flexibility to change the NAS IP address, the NAS path, etc. behind the scenes. As long as your drive mapping gets you to the correct place, MC doesn't need to know about any of these changes. For me, this is much easier than changing the IP and path any time there's a major NAS change.
Brian.