Is it disliked to clip one`s nails at night, and is it permissible to burn them afterwards?

It is desirable to bury the cut hair and the clipped nails. As for burning clipped nails, there is no evidence forbidding that , but it is better to suffice with the aforesaid ruling-burying cut hair and clipped nails-as it is based on a well known evidence.

Is hair extension permissible?

All Perfect Praise is due to Allah, The Lord of The Worlds 

It is impermissible for the man and the woman to apply a human`s hair as extension, but using artificial hair is permissible for the married woman after obtaining the approval of her husband, and provided that non-Mahrams (Marriageable men) don`t see her. And Allah Knows Best.

Is a wife considered sinful if she asked for divorce because her husband married another woman?

A second marriage is lawful, and so it is impermissible for you to ask for divorce because of that. If you are certain that you won`t be able to deliver Allah`s rights and those of your husband`s , then it is permissible for you to ask for Khul`a(Divorce on the demand of the wife). However, you should exercise patience since after difficulties, there is easiness by the will of Allah.

What is the ruling on having slight discharges of menstrual blood during a day of Ramadhaan, and before Maghrib time ?

A woman who is certain that her menses have started during a day time of Ramadhaan is in a state of menstruation, and her fasting is considered broken at first sight of blood. However, she is rewarded for not breaking fast at the beginning of day time.