Woman

We can not say that this story is authentic at all though it is claimed by non Muslims. The great prophet Jesus (AS) will never allow a non Mahram woman to touch him.

Stories claimed by non Muslims should never be taken for granted but we must search for authentic sources if any before accepting it.

Wassalam.

Helping people in need is very much encouraged in Islam. Female doctor who help people in need in any humanitarian mission will be rewarded just like male doctor who help people in need. Hijab and abiding the Islamic rules is compulsory in every Muslim female. Father's consent is necessary if she is unmarried as well as husband's permission if she is married.

Wassalam.

No, she does not need to redo her prayers. Ghusl itself is not obligatory if she was not sure that she had the real climax discharge while she was asleep. Only remembering the dream does not mean that she had the climax discharge. 
'Wassalam.

Applying medication for medical necessity is allowed as much as it is really necessary but it should not look like beautification at all. Muslim woman is not allowed to expose he beauty in front of the outsiders.

Wassalam.

Virgin girl does require in her marriage the permission of her father or her paternal grand father. If father and the paternal grand father refuse proposal of marriage with out valid Islamic reason when the proposal is from a Kof’ (Compatible believer) and the girl needs to marry to save herself from sin, then the condition of the father’s permission or paternal grand father’s permission will not remain. That is when the refusal of the father or his father is not based on a valid Islamic rules.

Wassalam.

Man and woman should not pray together on the same line. She is not allowed to pray ahead of him even if she was a Mahram for him.

She should be during prayers behind him that her place of Sojood (prostration) should not be ahead of the place of his knees during his Sojood.

Wassalam.

Your adopted sister is not your real sister, so, you are not allowed to look at her unclothed. Hijab rules apply on you and her .

Emergency has got its own exceptions just like emergency rules to save life of any other female who is non Mahram to you.

Wassalam.

Any man who commits the major sin of fornication with a married woman will be forbidden from marrying her for all his life. He can marry with another woman if she agrees but not that woman with whom he committed the crime of fornication while she was married even if she is now divorced or widow.

Wassalam.