Do coverings, bedding, and what the body touches become impure as a result of ritual impurity? And is it necessary to purify them before using them again?

All praise is due to Allah for your repentance and your awakening. The preponderant opinion is that semen is pure. It is not necessary to purify furnishings and objects unless you are certain that they have been afflicted by an impurity to the extent that you could swear by it. What you are unsure about does not require purification. If you are certain that something has become impure, purify it if you wish to pray on it, by drenching the impure spot with water until the impurity is removed.