Thanks Goldtop! Meanwhile, I found out one important thing in the rules from this bank. If you leave and want to withdraw your money, you need a copy of your passport, but also an official document stating you are not married (or have your spouse's signature officially verified!), and an official document stating where you live. My gemeinde states that the status of being married/or not needs to come from your heimatsort (place of origin?) not where you live. If this means I need to get a copy from my country, this whole process is way to complicated. (Also, if these forms/copies all need to be official, it will cost at least 3 times 20 CHF or more).

However, if you are leaving, but are clever, and transfer your funds to a kanton with low taxes on pillar 3a just before you leave, this bank only needs your signature and a confirmation of your new pillar 3a. What I do not know is if other funds also require the confirmation of not being married form...

I emailed this bank, and they replied. There are no costs associated with neither closing or transferring the account. They basically say, at least not at the moment, and probably won't be until others start doing the sme.