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.

Is prayer nullified by having thoughts while performing it?

Prayer isn`t nullified by having thoughts while performing it, provided that the praying person offers all of its pillars and meets all of its conditions. However, the reward decreases significantly in the absence of reverence since a praying person is rewarded according to the attentiveness of his/her heart during prayer.

What is the ruling on a woman shaking hands with the brothers of her husband`s father, and not putting on Islamic wear before them?

The aforesaid are strangers to the their brother`s son`s wife, therefore, it is forbidden for her to take off her Islamic wear before them, or to shake hands with them.

What is the ruling on the cessation of blood after (40) days from delivery, but later continued sporadically during two days of Ramadan?

Once postpartum bleeding (Nifas) ceases, and the woman is certain that it won`t reoccur, then she becomes ritually pure and so she is free to make Ghusl (purificatory bath), pray, and fast. If the bleeding reoccurs before fifteen days from its cessation, and before the end of (60) days after delivery, then the ruling on postpartum bleeding is effective, and her fasting and prayer are null and void, thus she must make up the fasting that she missed and not the prayer during those particular days.