Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
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.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
If the menses lasted for over than 9 to 10 days, considered menstruation?
If the duration of the bleeding does not exceed fifteen days, it is all considered menstruation, even if the usual pattern changes.