Is a menstruating woman obliged to pray during menses, and should she make up missed prayers?
All perfect praise be to Allah, The Lord of The Worlds A menstruating woman is prohibited from prayer during her menses, and she isn`t obliged to make up missed prayers. And Allah Knows Best.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
Does touching women temporarily forbidden in marriage nullify ablution?
It is prohibited to touch, or to shake hands with such women as they are considered strangers, and doing so nullifies ablution.
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.