Is the `Iddah (waiting period) of the divorced effective from the time the divorce took place, or from the time of registering it at the court?
It is considered effective from the very moment her divorce took place, but not from the time of registering it at the court. And Allah Knows Best.
What is permissible for the person who wants to ask for a woman`s hand in marriage to see from her body?
He is permitted to see her hands and face only, but if he wants to see more, then he has to send a woman that he trusts to do so.
Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?
The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.
Is speaking to a person from the opposite sex forbidden or not?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Talking to a person from the opposite sex is forbidden in Islam because it entails a great deal of evil, which could lead to a graver sin. Moreover, Islam forbids having a friend from the opposite sex. And Allah The Almighty Knows Best.
