All third country citizens entering the Schengen Area are required to have adequate funds and health insurance to cover their visit. Each member state sets it’s own limits and is the same as for the visa application - 100 Frans per day.
I don’t think it is checked very often. I only read of one student being checked and she didn’t have the funds and had intended to work!
The “several years” part is not correct. I know a bunch of guys who in no time brought over women whom they had just met when on vacation in South America and in Asia. And in the cases of some of these guys, they didn’t even propose to or marry the woman until over a year from the date on which the woman moved in with him in Switzerland!
That's generally not true. If the parties involved declare their intention to marry, the party living in Switzerland has a right to family reunification (i.e. a C permit or citizenship), has the adequate financial resources to support the other person during marriage preparation and for family reunification and the correct documentation is submitted (birth certificates etc.) then the authorities are really obliged to issue a marriage visa.
There are no requirements on the relationship duration or depth, Switzerland is not Israel
Yes, there are law paragraphs concerning sham marriages and some cases will be more subject to scrutiny than others but as far as I have seen it's mostly cases when there's a huge age difference and/or when the incoming person is from a country producing a lot of refugees and there's no evidence of a long relationship etc. A US person moving in to marry a Swiss one is unlikely to raise such red flags IMO.
Their girlfriends (eventually wives) did not enter Switzerland illegally. They applied for and received long stay visas from their local Swiss consulates before entering Switzerland, and once in Switzerland received residence permits allowing them to work. Their inclination to work was another matter. The cantons included Geneva, Luzern, Ticino, and Valais.
And a couple of my husband’s work colleagues took several years before they were able to get the marriage/permit agreed. I think another one did it pretty quickly, but it really depends on individual circumstances and probably the canton you’re applying in as well.