How can a mattress that has become ritually impure due to madhy (pre-seminal fluid) and maniy (semen) be purified? And does this impurity transfer to the carpet and other parts of the house when walked upon with a wet foot, thereby affecting the validity of the prayer?

According to the preponderant opinion, semen is pure, but it is better to wash it to avoid differences of opinion. As for madhi (pre-seminal fluid), it is impure and is purified by pouring water over the site of the impurity until it covers it. If the impurity of madhi is covered with water, the bedding becomes pure, and the carpet or feet do not become impure by touching water splashes from it. Prayer on it is valid. It is advisable to disregard obsessive thoughts and be lenient with oneself.