Is it incumbent on a wife whose husband hasn`t gone to bed with her (for sexual intercourse) for many years to observe `Iddah (waiting period) upon his death?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhmmad and upon all of his family and companions.

Upon the death of the husband, a wife is obliged to observe the `Iddah even if he hadn`t slept with her because she inherits him. And Allah Knows Best.

Is it permissible to fast on behalf of the dead who died owing missed fast to make up?

His relative should fast on his behalf, and it is permissible for the guardians to give permission to non-relatives of the dead to fast on his behalf as well. And Allah Knows Best.

Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?

It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.

Is it permissible for a wife to leave her house without asking her husband?

It is impermissible for the wife to leave her house without asking her husband except for a sound reason.