As far as I know, this will not happen until after you have been here for three months. However, after that time you will be billed for those previous three months in addition to future months with the randomly chosen company.

Sorry, I don't know what the restrictions are on substituting Swiss health insurance with travel insurance. It is certainly possible because there was something written about it in a welcome booklet for interenational students that I read. Hopefully other people on here can providce you with more details.