I think this translation is misleading. The intonation of the spoken words are not really clear and for me do not sound like a question. Wouldn't it be better to translate this as "We are writing a letter" or alternatively add "czy" or adjust the intonation?
Does it still make sense if i use pronouns for we in Polish to me you or you guys ? Because in english I'd say something like, "Are we going to the gym ?", to refer to one specific person. I was wondering if this could be used in Polish.