What is teh ruling on thoughtless oath?

One who swears by Allah unintentionally and isn`t determined to fulfill his oath, nothing is due on him. Allah, The Almighty, Says (What means): "God will not call you to account for thoughtlessness in your oaths, but for the intention in your hearts; and He is Oft-forgiving, Most Forbearing." [Al-Baqarah/225]. However, it is dispraised for a Muslim to swear frequently.

Is a woman`s face an Awrah (a private part) that should be covered?

During prayer, a woman`s whole body is a private part except the hands and the face. Outside the time of prayer, scholars are of the view that a woman should wear on her Islamic attire to avoid temptation.

Is it permissible for the big brother to force his sisters to wear Hijjab (Islamic wear) if their father didn`t do his part in this regard ?

All Perfect Praise is due to Allah, The Lord of The Worlds

The father`s attention should be drawn gently and politely, and the sisters should also be reminded with good words since Allah, The Almighty, Says (What means): "O ye who believe! Save yourselves and your families from a Fire whose fuel is Men and Stones." [Al-Tahreem/6]. And Allah Knows Best.

Is Fajr (dawn) Sunnah a confirmed one?

All praise be to Allah The Lord of The Worlds                                                                                                                                                                                  Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.