Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
What is permissible for the husband to do as far as having sex with his wife is concerned?
The couple are free to enjoy each other sexually provided that they don`t do it during menses. It is also forbidden for the husband to enjoy the wife from her anus.
My maternal aunt`s son is living abroad; however, both our families have recited Al-Fatehah declaring our engagement. We have been engaged for three months, but the marriage contract wasn`t concluded because he couldn`t come to Jordan since my mother and brothers are abroad. Is it allowed that he sees my picture without Hijab knowing that the marriage contract will be concluded at the first opportunity?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
Betrothal is a promise to marry, so your betrothed is a stranger to you and isn`t permitted to look at you even through a picture. Once your marriage contract is concluded, you become husband and wife and he can look at you as much as he wants. Moreover, he may deputize his father to carry out the procedures of the marriage on his behalf. And Allah The Almighty Knows Best.
Is it incumbent on the fiancée to obey her fiancé?
When the woman settles in her husband`s house, it is incumbent on him to provide for her and it is incumbent on her to obey him. Before that, and if the marriage contract had been concluded, then she is lawfully his wife and thus she should abide by custom in treating him, but if the marriage contract hadn`t been concluded, then she should treat him as a non-Mahram (Marriageable).