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.
Is it permissible for a financially capable woman to pay the Zakat to her sons or one of them?
It is permissible for a mother to give her children from zakat if they are eligible to receive it, even though she is obligated to provide for them. This is based on the saying of the Prophet Muhammad (PBUH) regarding Zainab, the wife of Abdullah Ibn Mas'ud (may Allah be pleased with them): "Your husband and your children are more deserving of your charity" [Al-Bukhari]. And Allah Knows Best.
Is it permissible for a woman who is in her confinement to fast upon seeing blood signs that are neither black, nor red ?
Brownish, reddish, and yellowish discharges are all considered confinement until there is no colored discharge which marks the end of confinement. Moreover, the aforesaid woman is prohibited from fasting until she attains ritual purity. And Allah Knows Best.
Does bleeding from the body, such as from wounds, invalidate ablution?
Bleeding doesn't invalidate person's ablution. And Allah Knows Best.