Is it permissible for a Muslim woman to go out wearing adornment and not putting on her Hijjab(Islamic wear)?

It is impermissible for a Muslim woman to go out wearing adornment, and not having her Hijjab on.

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.

What should a woman who is in a state of menstruation, or confinement do if she became ritually pure during the day of Ramadhaan ?

If she became pure during the day time of Ramadhaan, it is desirable for her to fast the rest of that day, and to make up for it along with the days that she had missed due to menstruation.

What is the ruling on giving Zakah(obligatory charity)to one`s relatives?

It is impermissible to pay Zakah to one`s origins( parents and grandparents) because providing for them is an obligation on their branches (sons and daughters )if they were poor, but it is permissible to give some of the Zakah money to relatives whose provision isn`t due on the giver of the Zakah.