السلام عليكم ورحمة الله وبركاته Does the family of the one who is sacrificing abstain from cutting hair and nails or just the sacrificer? Also since Eid is on Friday, is the Friday prayer still obligatory? If not what is the ruling on it? May Allah reward you.

Only the one sacrificing/paying for the sacrifice. Imam Ibn Baz mentioned that: It is better to perform the Jumuʿah (Friday) prayer, because the Prophet ﷺ used to perform both the Jumuʿah and the ʿEid prayers. However, concession is made to the people who attended the ʿEid prayer: whoever wished could attend the Jumuʿah, and whoever wished could pray Ẓuhr instead. The Prophet ﷺ used to perform both.