1)If I and my family are guests in a friends house for shabbos,can I light chanuka candles (of my own) while being a guest and be motzi the rest of the family in chanukah or does that only work in the classic case of ner ish ubeiso?
2) Can one give a peruta to an owner in a case where the giver of the peruta also co-owns the house or can only a guest give a peruta to join in the mitzva?
1) If you do the lighting, you can fulfill the mitzvah on behalf of your family. There is no reason why this will not apply in your “new home” as guests any less than in your own home.
2) Even a co-owner can give a perutah. The mefarshim debate the rationale for giving a perutah (of an achsanai). According to one opinion, a person must own part of the Chanukah lights. According to another opinion, the principle is that paying gives a person a connection to the lights. Both rationales apply to a partner.