Are phone conversations between the two sexes permissible if for consultation, and within the limits of good manners?
Such act is impermissible since it renders hearts corrupt, and could lead to forbidden attachment. Allah, The Almighty, Says (What means): "and follow not the footsteps of the devil." [Al-Baqarah/68].
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 the ruling on a Muslim who slaughters an animal while being in a state of Janabah (ritual impurity)?
All Perfect Praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upo all of his family and companions.
Slaughtering is permissible for the ritually impure man and the menstruating woman because ritual purity isn`t a condition for the validity of the slaughtering. Moreover, it is permissible for the uncircumcised person to do the slaughtering as well. And Allah The Almighy Knows Best.
What is the Ruling on Reciting the Prophetic Narration?
All Perfect Praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
Reciting the Prophetic narration is permissible as many scholars used to, since in principle, the rulings of recitation have to be observed while speaking Arabic language. And Allah Knows Best.