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.
Does passing wind from the anus affect ritual purity?
Ablution is nullified by the passing of wind from the anus, but washing the anus is not required as wind leaves no impurity.
Is it permissible to divide the Aqeeqah amongst one`s brothers and family?
Giving a portion of the Aqeeqah, even a small one, to the poor and needy is obligatory, and if one`s brothers and family are among the needy then, they are more entitled to it, and this way it is a charity and an observation of kinship ties. However, if they aren`t needy then, it is permissible to give them from the Aqeeqah after giving the poor and needy their share.
Is it permissible to perform Tayammum for a month due to a medical condition that requires avoiding water?
Tayammum is permissible so long as the above excuse lasts. And Allah Knows Best.