Is It Permissible to Divorce One's Wife for not Praying
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
You should do your best to save her from hellfire by making her observe daily prayers on their prescribed times, even if this means giving her a generous incentive. However, if she insisted on her position, then it is permissible for you to divorce her. And Allah The Almighty Knows Best.
Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
Is it permissible for a woman who has become pure before the end of forty days of confinement to perform different acts of worship? and is it lawful for her husband to have sex with her?
Once postpartum bleeding ceases and she is certain that it won`t happen again, she becomes pure, and so she should perform Ghusl (ritual bath), pray, and fast. She can also have sex with her husband even before the end of (40) days because the minimum of postpartum bleeding is a moment, and the maximum is (60) days. However, the postpartum bleeding for the majority of women is (40) days, but this does not apply to rest of them.
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.