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.
What is the age of the Aqiqa or the Udhiyah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The minimum age for a sacrificial animal (Udhiyah) and the birth sacrifice (Aqiqa) is as follows:
Camels: Five years old, entering their sixth year.
Cattle and Goats: Two years old, entering their third year.
Sheep: One year old, entering their second year; however, it is permissible for a sheep to be six months old provided it is large in size and plump.
And Allah the Exalted knows best.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
What is the ruling on performing Tarawih in sets of four rak‘ahs with only one Tasleem?
It is not permissible to combine more than two rak‘ahs with a single Tasleem in Tarawih prayer. Whoever does so, their prayer is invalid. Shaykh al-Islam Imam Muhammad al-Ramli (may Allah have mercy on him) stated: "If a person prays four rak‘ahs of the Tarawih prayer with a single Tasleem, it is not valid if they did so intentionally and with knowledge [of the prohibition]. Otherwise, it becomes an 'absolute voluntary prayer' (nafl mutlaq); because it is contrary to what has been prescribed." [Nihayat al-Muhtaj, Vol.2/P.127].