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.
Is it permissible for a woman to wear underwear while performing Umrah?
Yes, it is permissible for a woman to wear underwear while performing Umrah. This is because she should keep her regular clothes that cover all her body while being in a state of Ihram (ritual consecration) for Hajj, or Umrah. However, she should uncover her face and hands, but it is permissible for her to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.
Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?
It`s impermissible to offer Salah on behalf of the sick, or the dead.
How should I deal with the whispers of the devil with regard to ablution and purity?
Whispers in ablution are from the devil, and so you should take refuge in Allah from the devil`s evil suggestions that aim to distort the religion. Thus, once an organ is completely pure, don`t question its purity since having whispers doesn`t mean that the purity is invalid as it has already been established.