Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
A pious man proposed to me and my father was hesitant in this regard because he is black, am I sinful if I accepted his proposal?
If the suitor is pious, color isn`t a drawback. However, try talking to your father kindly, so that he approves of your marriage with contentment, and that is better for you.
When is Istikharah (guidance prayer) Du`a offered, before Tasleem (saying asalamu alikum warahmatu allah wa barakatuh to end the prayer), or after it?
It is offered after Tasleem.
Does smoking break the fast?
Yes, smoking breaks the fast because smoke particles intentionally enter the lungs, which are considered part of the body cavity (jauf).