All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
A pubescent woman is obliged to wear the required Hijab with the conditions mentioned in Fatwa: 83702 when going out of her home. It is forbidden for her to show any parts of her body, neither her arms nor her legs, nor her hair nor anything else. We have already issued Fatwa: 83033 clarifying the obligation of the Hijab and its backing evidences from the Quran and the Sunnah, so please refer to it.
As regards when she is in front of her Mahaarim (plural of Mahram, that is, a person whom one is permanently prohibited from marrying due to suckling, marital, or blood relations), there is no harm for her to show what usually appears when she is doing her housework, like her arms, her legs, her hair, her neck and so forth. She is not obliged to wear the full Hijab in front of them as long as she is safe from temptation.
As regards shaving the hair that grows on the arms, there is no harm in removing it. The hair of a person is divided into three categories:
1. The hair which Islamic law forbids us from shaving, like the eyebrows.
2. The hair which Islamic law encourages us to shave, like the hair that grows under the armpits and the pubic hair.
3. The hair which Islamic law has kept silent about - it neither forbids us from shaving it nor does it order us to shave it - like the hair of the thighs, legs, chest, and arms; a person has a choice either to shave it or to leave it.
As regards writing with the left hand, we do not know any evidence that prohibits it and it is not permissible for anyone to forbid something except with evidence from the Book of Allaah or the Sunnah of the Prophet , or the consensus of the scholars . As far as we know there is no evidence stating that a person who writes with the left hand is a devil. However, dealing with the right hand in all good matters is a recommended act. The Prophet liked to use the right hand when he wore his shoes, combed his hair and when he purified himself [performed ablution or a ritual bath], and in all his (other) matters. [Al-Bukhari and Muslim]
Allaah Knows best.