Right, but it's part of the Schengen area, which also covers most of the EU countries, so once you got a visa to e.g. France, you're free to work and live in Switzerland as well.
Nope. There are many different types of Schengen visa [1] and it generally does not allow you to work. For this you need a national visa from a specific member state [2]. So, no, if you get a work permit in France, you are not free to live and work in Switzerland. In fact, EU citizens generally need a residency and work permit if they wish to live and work there.
From the page: "For employment lasting longer than three months, a residence permit is required."
I named their permit incorrectly: should be "residence permit" instead of "residency and work permit". The point remains that EU citizens generally need an official permit to work in Switzerland.
Switzerland is not part of the EU nor Schengen. Eu citizens can travel visa-free to Switzerland, but they can't work there. Same goes for US and many other nationals...
Wrong. You can enter Switzerland with a Schengen visa as a tourist. Finding work in Switzerland is difficult (employer has to prove it can't hire Swiss citizen for this position).