What is the ruling on praying while wearing shoes?

Is it permissible to combine and shorten prayers at home before traveling?

It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.

What is the ruling if a postpartum woman becomes pure before forty days; are acts of worship obligatory upon her, and is she permissible for her husband?

If the postpartum woman becomes definitely pure before forty days, she must perform the ritual bath and perform acts of worship as a pure woman does. What was prohibited for her also becomes permissible, so she becomes permissible for her husband after her bath. The minimum duration for postpartum bleeding is a moment (an instant), and its usual maximum is forty days. Reaching forty days is not a condition; rather, it is sufficient for the blood to stop or to see the white discharge (qassa bayda'). And Allah the Almighty knows best.

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.