There are some US citizens working at BBP. In fact, inside our section we have two people who were previously working in the US.

Even though the process to bring somebody to work in Switzerland is more tedious than for EU citizens, it is duable.

I would still fully recommend to apply if you are willing to relocate, without worrying about the administrative factor.

Yes they do. It makes the process more complex and lengthier though, so they'll most likely focus on Swiss/EU/EEA candidates.