What is the ruling on residual urine inside the urethral opening after purification (istinja'), and is it excusable, especially if it emerges after a period and only comes out with straining or manipulation? And what is the ruling on the prayers I have performed with doubt about the emergence of this urine?

You are experiencing waswas (obsessive whisperings), and you must ignore these whisperings and turn away from them. Do not pay attention to doubt or the sensation of something exiting unless it reaches the level of certainty. Any impurities inside the exit point have no ruling and do not require purification until they emerge. What remains inside the opening of the male organ has no ruling unless you are certain of its exit. Be careful not to expose the inner part of the exit point, as scholars have warned against this, saying it is a cause of waswas.