Is prayer valid if one feels something exiting the urinary meatus without the presence of wadi, and is it obligatory to inspect to distinguish between wadi and moisture, and what is the ruling on the purity of what exits?

If you doubt that something has exited from you, you are not required to inspect it, so as not to open the door to obsessive doubts (waswasah). Act based on the original principle, which is that nothing has exited. Your ablution (wudu') is not invalidated unless you are certain that something has exited. If something exits and you doubt whether it is wadī (pre-seminal fluid) or vaginal discharge, then choose and assign to it the ruling you wish. Both invalidate ablution, but vaginal discharge is pure if it exits from the birth canal, whereas wadī is impure. If you doubt what has exited, perform ablution in any case. If you wish, you may wash what it has touched, considering it wadī (which is more cautious). If you wish, you may consider it vaginal discharge, in which case you are not required to perform istinjā’ (washing after relieving oneself) from it. Your prayer is valid as long as you are not certain that something invalidating purity has exited, and close the door to obsessive doubts.