It's not the population cap, but that bilateral agreements with the EU depend on the free movement of people. Without it, Switzerland could lose access to the EU market, which accounts for 51% of their exports. Switzerland cannot just choose whatever they like from the agreements and cancel what they don't. They will have to accept whatever in order to keep in the EU common market, or the country will suffer massive troubles. Switzerland needs the EU much more than the other way around.
Plenty of us remember when Switzerland was not in the Schengen though. This might be good for Americans, who haven't been able to get working visas in Switzerland since EU countries now have priority. But otherwise, I don't see much changing beyond border procedures.
True, maybe. It is really hard to say. I'm not pro leaving in any sense (beyond being an American who used to work in Switzerland and wouldn't have that chance today because of the Schengen).
Most of the downsides would be on the goods side. Swiss companies would loose market access and the chance of "better" trade agreements is even worse then the UK, especially currently.
When you drive through there is someone standing looking at the line of cars and if they don't like the way you look they point to the side and you have to explain yourself and your cargo. It's like an arbitrary border control right now.