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 a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?
A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.
Is the one who doesn`t offer prostration of recitation during Quranic recital considered sinful?
Prostration of Quranic recital is a Sunnah due on whosoever recites a verse that contains a prostration. It is also a Sunnah for the reader and the listener. However, none of them is considered sinful for not offering it, but they deprive themselves from a great reward. It is obligatory to offer the prostration of Quranic recital in congregational prayer following the lead of the Imam.
Does wiping over one's socks during ablution permissible?
If the socks were thick, then wiping over them during ablution is permissible so long as wiping conditions are observed. And Allah Knows Best.