Is the prayer of someone who didn`t face Quibla (Ka`ba direction) valid?
All perfect praise be to Allah,The Lord of The Worlds. Facing the Quibla is a condition for the validity of prayer, and the prayer of the person who hadn`t faced the direction of the Quibla is invalid, and he is obliged to repeat it. And Allah Knows Best.
Is it permissible for a man to wear transparent clothing?
It is not permissible for a man to wear transparent clothing that reveals his 'Awrah (the area that must be covered). The 'Awrah of a man is "from his navel to his knees", and modesty is more prudent. 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.
What is Aqeeqah?
It is the sheep slaughtered on the seventh day from the child`s birth, and it is a confirmed Sunnah after the Prophet (PBUH).