Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?

It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.

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.

How does a praying person prostrate?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                        It is from Sunnah that he/she sits with both knees on the ground in order to prostrate, then hands, nose and forehead are placed on the same place. In addition, the toes have to touch the ground, and be directed towards the Qiblah (direction of Ka`bah) during prostration. And Allah Knows Best.

Is a woman`s neck an Awrah (private part)?

All Perfect Praise is due to The Lord of The Worlds.

It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams (Marriageable men). And Allah Knows Best.