Doubts with regards to urine

Q: I have a question about urine drops. I took my four year old to the toilet and I wiped her first and her urine dropped on my hands as I went to reach out for the water I'm not sure if the urine went anywhere else. It was a very small drop but I didn't think it would go anywhere up until I went to wash my hands.

Wife not hearing the talaaq

Q: I want to know that I gave talaaq to my wife once and then we revoked. After a year there was some problem again and I gave her Talaaq once. After about a week of second time, she started insisting with me that she did not listen that I gave her talaaq so it is not valid because she did not listen but I remember that I had told her talaaq one time. We want to know what Deen says in this case if husband say that he gave talaaq but wife says I did not hear? There was no other person at that time who can give testimony. Also, what Islam says that how we should proceed further as after revoking still there are fights and there is a chance that there may be talaaq again. I have asked my wife to sign a paper in front of Qur'an not to repeat those things which caused the fight because she did not want to bring any elder between us.

Committing zina

Q: If someone commits zina and then feels bad and wants to offer tauba and istighfaar with this hope that Allah Ta'ala will forgive him, but after tauba should he present himself before law authorities for Islamic punishment i.e sangsaar or not?

Applying nail polish

Q:

1. Is applying nail polish during haidh period permissible as we don't have to make wudhu to pray fardh namaz and when we make ghusl we remove it using nail polish remover?

2. Does applying nail polish amount to imitating kuffaar?

3. Can we use other make up items like lipsticks, mascara etc?

4. Are we allowed to dye (water proof dye) our hair other than black when in haidh period?

Obesity and overeating

Q: Please advise on the authenticity of the following:

(1) Narrated by Hadhrat Aaisha (Radiyallahu Anha) that she said: “The first calamity for this nation after the Prophet (Sallallahu Alayhi Wasallam's) death is fullness of their stomachs; when their stomachs became full, they became obese and their hearts weakened and their desires became wild.” - Bukhari

(2) Narrated by Anas bin Malik (Radiyallahu Anhu) that the Prophet (Sallallahu Alayhi Wasallam) said: “It is extravagance that one eats whatever he desires.” - Ibn Majah.

(3) If these are not authenticated, are they correct in their meanings?