Is it permissible to perform Tayammum for a month due to a medical condition that requires avoiding water?
Tayammum is permissible so long as the above excuse lasts. And Allah Knows Best.
Is it permissible for a woman to die her hair black?
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.
It is permissible for a woman to dye her hair with other than black at any time she likes, even during Ramadan since applying the dye doesn`t invalidate the fast. And Allah The Almighty Knows Best.
Who should pay the Zakah (obligatory charity) from the orphan`s money?
His/her guardian, and if the latter fails to do so, then the orphan himself/herself is obliged to pay the Zakah once he/she reaches puberty, and is capable of handling his/her own affairs. And Allah Knows Best.
Is touching a non-Mahram woman invalidates person's ablution?
Touching non-Mahram woman is prohibited, and according to the Shafiee's, it invalidates the ablution. And Allah Knows Best.