I assume you've had a letter from the uni telling you that you can do this postdoc? That's what you need to send a copy of as part of the documentation.

For 2 and 3, yes you need to write a document outlining your plans after you graduate, how you see your life developing over the next few years after graduation, etc, etc, and stating that you plan to do this in whatever country that isn't Switzerland.

https://www.ch.ch/en/retirement-or-study-switzerland/