What is the ruling on performing istinja' before every ablution?
Istinja' is not from the conditions for the validity of ablution. It is only obligatory for prayer when there is impurity from urine or stool on the private part, or if there is fear of the impurity spreading to the body or clothing. And Allah the Almighty knows best.
If the bleeding ceases after 40 days following childbirth, but then returns intermittently during two days of fasting, what is the ruling?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Whenever the post-natal bleeding (Nifas) ceases and the woman is certain it will not return, she has become pure; therefore, she must perform the ritual bath (Ghusl) and resume praying and fasting. However, if the blood returns within fifteen days of its cessation and before sixty days have passed since the delivery, the ruling of Nifas applies once again. Consequently, any fasting or prayer performed during that interval of purity is rendered invalid; she must make up for the missed fasts of those days, but she is not required to make up for the prayers. And Allah the Exalted knows best.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.