When is Istikharah (guidance prayer) Du`a offered, before Tasleem (saying asalamu alikum warahmatu allah wa barakatuh to end the prayer), or after it?
It is offered after Tasleem.
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 it permissible to listen to chants praising the Prophet if accompanied by musical instruments?
If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.
Is my son who was breastfed one filling time by my aunt considered a brother to her children?
The baby who was suckled five sporadic times by a woman is considered a son/daughter of hers.