They all leave for the wedding. The father, the two main characters and the grandmother all in traditional outfits. The bride in her gown and the groom in his suit. But, the next scene of them at the wedding, the bride and groom are still dressed as they were, but the others are wearing street clothes. Not sure if it is tradition to change out of the traditional outfits.
JJ would not be able to use the airline ticket as her and the other's Jessica Johnson's birth-date would also have to match. Their full legal name would also have to match, including any middle names.
There is no way Henrik can identify a bunad to be from Bergen. A bunad is regionally bound, each city does not have their own bunad.
Most of the language they speak "Norwegian" is not really proper Norwegian. For all Norwegians it sounds more like any foreigner that thinks they can speak Norwegians. It is insulting really.
Jessica states that she goes by JJ. It is unlikely that she then would have given her name to the barista as Jessica Johnson.