Does anyone have experience/advice for what do do if living within Switzerland, but working for a company that is solely doing business outside Switzerland, in this case USA.

I am a US citizen, so I already know I will have to pay US taxes. I assume, I will likely also have to pay Swiss taxes. I am just not sure what the legal basis is--considering that I will be earning money in the US directly to US bank account. Main questions:

1. Do I just self-report this income here in Switzerland?

2. Do I need to incorporate somehow? (It seems I am not Sole-Proprietorship, since I only have one client.)

3. Will my employer in the US be responsible for added expenses/insurances etc. to be able to pay me whilst I live in Switzerland?

Any advice or where to go for these types of questions would be great. I just went to my cantonal Ausgleichskasse and they told me just to mail them a copy of my contract and an explanation of the situation and they will mail it back. But I in principle need to know what the situation is before I know what the contract will be (i.e. if I am working as a separate entity here, or an employee in the US, the contract will be different).