What can I do to rid myself of recurring doubts about prostration, my feeling as if I am wrestling when prostrating, and the necessity of washing a cup after someone else has used it, due to my belief that if I do not do so, I would be drinking something unlawful?

We advise you to turn away from your whispers (waswas) and be keen on praying in the mosque with the congregation. Try to prostrate as much as you can. If you are unable, then gesture with your head, and make your prostration lower than your bowing (ruku'). As for drinking from a vessel from which another has drunk, it is permissible as long as the drink is lawful.