Is it obligatory to inspect clothing to ensure it has not been spattered with urine after relieving oneself, or is it sufficient to remove only what one feels? What is the ruling on the prayer of someone who prayed while fearing that his clothes might have been spattered with urine? And what is the ruling on things he touched thereafter?

You are obligated to wash off the urine spray that you see only on your hand and arm. Your clothes do not become impure merely by doubting they have been affected, and you are not required to search for it. Prayer with these clothes is valid.

The Malikis hold that sprinkling water (nadh) is obligatory if you doubt that impurity has touched something. If one intentionally omits the nadh, their prayer is invalid and must be repeated. However, if one omits it due to forgetfulness or inability, they only need to repeat the prayer within its prescribed time, and there is no penalty after the time has expired. The mosque carpet or the things you touched do not become impure as long as you are doubtful about them being affected by impurity and you have washed what you are certain of. It is advised not to pay attention to obsessive doubts (waswasah) and uncertainties.