What is the ruling on one who masturbated and then slept, then woke up for Fajr prayer while the Imam was praying and the weather was very cold, so he washed his private parts, performed ablution, and prayed, and he repeated this for Jumu'ah prayer and the rest of the obligatory prayers until 'Isha prayer, when he performed ghusl?

Masturbation is forbidden, and one must repent from it. Prayer while in a state of major ritual impurity (janabah) is invalid by consensus, and it becomes forbidden if done intentionally. One who wishes to pray while in a state of janabah must purify themselves with water. If unable to do so due to severe cold, they should perform tayammum (dry ablution) and pray to honor the time, then repeat the prayer when able to use water. This is based on the Prophet's (peace be upon him) saying: "Indeed, pure earth is a purifier for the Muslim, even if he does not find water for ten years. But if he finds water, let him touch his skin with it, for that is better." The Friday prayer should be repeated as four rak'ahs of Dhuhr prayer.