Is the prayer valid for someone who experiences a distracting thought about creed while heading to the mosque, or a distracting thought about religion during prayer? And do the hand of the laundromat owner or clean clothes become impure if they touch clothes that have dry and wet semen and prostatic fluid on them, and are placed in the same bag that contained the soiled clothes?

The questioner is afflicted with severe scrupulosity (waswasah), and answers will not benefit him as long as he indulges in it. He must strive against himself to قطعها (cut it off/stop it). The questioner is not held accountable for these whispers because a servant is not held accountable for inner thoughts (hadith al-nafs). There is no ruling that the washer's hand or the clothes become impure after washing simply by placing them in the previous bag. The clothes are pure, and it is permissible to pray in them.