This is in Sweden, right?
Is this bankid-thingy completely closed, then? Any possibility to get open API's for it since I think it has something to do with the new EU-legalization on opening the service API's of banks...?

Any posibility to take it up for opening, if it is tightly closed? I think you have pirate-party in Sweden that has some representation in your government and unless I am mistaken the party agenda is against all kinds of closed SW generally; should be more so if said technology is something people depend in everyday life.