Is it Islamically impermissible to pray at home? And how does one make up missed prayers? And what is the way to get rid of masturbation and save oneself from the torment of the grave and Hellfire?

Abandoning prayer is one of the gravest sins; in fact, some scholars consider it an act of disbelief (kufr). Omitting even a single prayer is worse than committing adultery, theft, drinking alcohol, or taking a life. You must hasten to sincere repentance. Your prayer at home is valid and fulfills the obligation, although you incur sin for abandoning congregational prayer. However, this is less severe than abandoning prayer altogether. Strive to perform prayers in congregation at the mosque. If you have a valid excuse that prevents you from going to the mosque, then there is no sin upon you for praying alone. If you pray in congregation at home with your family, that is sufficient. You must maintain prayers at their appointed times. There is a difference of opinion among scholars regarding the obligation to make up missed prayers. You must perform ghusl (ritual bath) if semen is discharged from you, whether through masturbation or otherwise. Masturbation is forbidden, and you must repent from it. What will help you abandon it is marriage, or increasing fasting, supplication, occupying your free time, associating with righteous people, and avoiding provocations.