What is the ruling on the prayer of one who doubted whether water reached his fingers when washing his hands during ablution, or whose young sister passed in front of him while he was praying, or who doubted the emission of pre-seminal fluid (madhy) during prayer, then performed ablution and prayed?

It appears from your question that you are afflicted with obsessive whispers (waswasah). We advise you to disregard them and pay them no attention.

Regarding your first question: If the doubt about water not reaching between the fingers arises after completing ablution, then it should be ignored, and your prayer is valid. However, if you know or strongly believe that water did not reach a part of your hand, then your ablution is invalid, and so is your prayer. In this case, you must repeat the ablution and all prayers you performed with that ablution.

Regarding your second question: A child passing in front of you does not invalidate your prayer. However, one should be keen on praying towards a sutrah (an object placed in front of the worshipper as a barrier).

Regarding your third question: If you doubt the emission of madhiy (prostatic/vaginal fluid), the default is that it has not been emitted, and you are not required to purify yourself or repeat ablution. If you are certain that something has been emitted but doubt whether it is madhiy or vaginal discharge, you may choose and assign it the ruling of whichever you wish. Vaginal discharges are pure according to the preponderant opinion, even if they nullify ablution.

We reiterate our warning to you about obsessive whispers and the necessity of striving against them.