What is the ruling on prayer and purification, and is إعادة (repetition) obligatory for one from whom drops of urine exited after استنجاء (washing after defecating/urinating) without him knowing or feeling it, and is he considered a person with an excuse, and does he fall under the threat mentioned in the noble Hadith?

The cure for obsessive whispers (waswas) is to ignore them and not pay them any attention. If you doubt that urine has exited, do not pay attention to the doubt, and do not repeat the cleansing (istinja) or purification (tahara). Your prayer is valid and accepted. However, if you are certain that something has exited, then you must purify yourself and perform ablution (wudu').