Is it permissible for the mother to give her children from the Zakah (obligatory charity) of her money?

It is permissible for the mother to give her children from the Zakah of her money if they are Zakah-eligible recipients, and she isn`t obliged to provide for them.

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.

What is the ruling on one who sees moisture on his clothes and doubts whether it is semen or pre-seminal fluid (madhy)?

Whoever finds moisture upon waking from sleep and doubts whether it is semen or madhy, and cannot distinguish between them, he may choose between them and act according to his choice. If he wishes, he can consider it semen and perform the ritual bath, or consider it madhy, perform ablution, and wash what it has soiled. This is because if he fulfills the requirement of one of them, he is definitively free from it, and the default is his innocence from the other. And Allah the Almighty knows best.

Is it permissible to slaughter a sheep on Eid al-Adha with the intention of charity (sadaqah) on behalf of a sick person, and with the intention of udhiyah (sacrificial animal) at the same time?