Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it valid to have Suhoor before sleeping, even if it is before midnight?
Suhoor refers to the pre-dawn meal eaten after midnight to help a Muslim endure fasting. The closer it is to Fajr, the better.
The Prophet ﷺ said: "My Ummah will remain upon goodness as long as they hasten to break the fast and delay Suhoor." [Narrated by Ahmad]
This is because delaying Suhoor makes it more effective in providing strength for worship. However, if there is a risk of Fajr entering while eating, one should refrain from Suhoor out of caution.
The Prophet ﷺ said: "Leave what makes you doubt for what does not make you doubt." [Narrated by Al-Tirmidhi]
Is a woman sinful if she fasts out of shyness from her family while menstruating or in postnatal bleeding?
It is forbidden for a woman who is menstruating or in postnatal bleeding to abstain from food and drink with the intention of fasting. If she fasts out of shyness, she is sinful, as her fast is not valid.
However, if she refrains from eating and drinking without intending to fast, it is not forbidden, but she unnecessarily burdens herself without need.
What is the ruling on entering the toilet with something containing the remembrance of Allah?
It is disliked to bring into the toilet anything containing a reminder of Allah, such as the Quran or a sacred name (like the name of Allah, Muhammad, etc.). If one does that, etiquette dictates that he conceal it so it is not visible while entering the toilet, either by cupping his hands over it, putting it in his pocket, or inside his shirt if it is a necklace or ring. And Allah the Almighty knows best.