Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
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.
Can a person required to give kaffarah feed it to their own family members?
The kaffarah must be given to the poor and needy who are not financially dependent on the one giving the kaffarah.
If a person feeds it to their own family members, it does not count as kaffarah, and their obligation remains unfulfilled.
Is it valid to perform the obligatory prayer while sitting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Standing (Al-Qiyam) while having the ability to do so is one of the pillars (Arkan) of the prayer; the obligatory (Faridah) prayer is not valid without it. However, whoever is unable to stand may pray sitting down. As for voluntary (Nafilah) prayers, it is permissible to pray them sitting even if one is able to stand, but the one sitting receives half the reward of the one who prays standing. And Allah the Exalted knows best.