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 it permissible for a Muslim to slaughter an Aqeeqah on behalf of someone else, and offer it to him as a gift?

In principle, the guardian is the one who should offer the Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) because he is obliged to provide for the newborn, and it is impermissible for anyone else to slaughter it on his behalf unless with his consent. However, it is permissible for a person to offer the sheep, or its price as a gift to the guardian of the newborn, and then the latter can slaughter it, or deputies someone else to do that on his behalf.

Is it permissible for a wife to leave her house without obtaining the permission of her husband, and not to come back unless he divorces her co-wife?

It is forbidden for the wife to leave without obtaining her husband`s permission, and it is impermissible for her to ask him to divorce her co-wife as this inflicts harm on the latter and such an act is forbidden in Islamic law.

What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?