A frum family has a non-Jewish young adult (post-college) who lives with them and participates in family life (more than a boarder). How do we think about בישול עכו״ם for them from things he cooks?
That’s a tough one, because there aren’t even the kulot of when it is of a commercial nature, etc. I’m not sure what I could advise other than – in special circumstances – NB: NOT saying this as regular pesak – we could adopt a very broad category of נאכל כמות שהוא חי (like, do we consider fish in that category, since people eat sushi?), and a very narrow category of עולה על שולחן מלכים (like, if you make a fancy rice dish by first cooking plain rice, then adding stuff to it, or something like that with chicken, etc. – well, at the time it was cooked, when it would have gotten the status of bishul akum – it wasn’t yet oleh al shulchan melachim. I in general consider that category to be what they would serve at a schmorg).
Also – the language of Shulchan Arukh YD 113:1 is ללפת בו את הפת – which Rav Yosef Eliyahu Henkin explains it pretty literally as only something that is eaten together with bread, not something that is eaten as a staple part of the meal to fill you up. See here.
Whether there is beli’at keilim (or beli’ah in general) by bishul akum is a question, since the concern of social interaction is not so relevant here, and there is also a question if Chazal made this an issur gavra or an issur cheftza. Specifically the issue of beli’at keilim is a machloket rishon – see Tur and Beit Yosef YD 113. Shulchan Arukh YD 113:16 states that it is forbidden and then says yeish omerim that it is permissible. The general assumption is that he is being strict, but a number of poskim think that the matter is not resolved, and there is good reason to be lenient after 24 hours – see Pri Chadash no. 25, and in particular Pitchei Teshuva 6 in the name of Chokhmat Adam. Also, the Ra’ah (Bedek HaBayit 94a) permits the beli’ah when the non-Jew cooked for him/herself, because then there isn’t a problem of חתנות.