Is it permissible to pay the Fitr Zakah(obligatory charity) of Ramadhaan on behalf of a dead person?

The Fitr Zakah of Ramadhaan isn`t due on one who had passed away before the sunset of the last day of Ramadhaan.

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.

What`s the ruling on using the following materials in manufacturing cosmetics: olive oil, Vaseline, talc powder, glycerin, honey, almond oil, pine oil, galingale and marjoram?

All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

None of the above materials is forbidden, and it`s lawful to use them in manufacturing products that are beneficial to people. This is because, in principle, all things are lawful so long as there is no evidence in Sharia indicating otherwise. And Allah Knows Best.

Is it permissible for a person who is in a state of Janabah(Ritual impurity) to clip his nails, or to cut his hair?

It is permissible for those in a state of Janabah and menstruation to clip their nails and to shave whatever hair that is permissible to be shaved.