What is the ruling on one who performs ablution or the ritual bath while having nail polish?
Nail polish must be removed before ablution or ritual bath so that water reaches what is beneath it, because it is a barrier that prevents water from reaching that area. This is based on the hadith narrated by Ali (may Allah be pleased with him) from the Prophet (peace be upon him): "Whoever leaves a hair's breadth of his body unwashed from major impurity, such and such will be done to him in the Fire." (Reported by al-Bukhari). And Allah the Almighty knows best.
What is the ruling on one who sees moisture on his clothes and doubts whether it is semen or pre-seminal fluid (madhy)?
Whoever finds moisture upon waking from sleep and doubts whether it is semen or madhy, and cannot distinguish between them, he may choose between them and act according to his choice. If he wishes, he can consider it semen and perform the ritual bath, or consider it madhy, perform ablution, and wash what it has soiled. This is because if he fulfills the requirement of one of them, he is definitively free from it, and the default is his innocence from the other. And Allah the Almighty knows best.
When is Istikharah (guidance prayer) Du`a offered, before Tasleem (saying asalamu alikum warahmatu allah wa barakatuh to end the prayer), or after it?
It is offered after Tasleem.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.