Using one's stepfathers name in the nikaah certificate

Q: I am getting married in July. My mother has done 2 marriages. She is separated and divorced from her first husband long time ago. I was born from her 2nd husband. Not keeping any difference, she and my real biological father kept the name of her first husband as my fathers name.

All my life, my education, identity card everything is made on his name. In my nikaah, my wali agreed to be there but in the nikaah nama (cerficate) the name of my stepfather would come and not my real father. Would my nikaah be valid?

Doubts regarding ghusal

Q: What if I do ghusal and then also attend salaah but later I have a doubt whether the ghusal I did was valid or not. The reason being that I think the water didn't wet all the hair on my body. Should I do the ghusal again and repeat the salaah which I attended?

Feeling jealous if husband takes a second wife

Q: Allah created both men and women differently such that a woman does not naturally feel to have more than one spouse at a time.

1. My question is that if it was in the nature of a male to have more than one wife as created by Allah then why are there naturally the feelings of jealousy or insecurities and intolerance that a woman feels about it? My mind and heart both know that Allahs plans are the best and I blindly trust in them but then why I feel annoyed and really bad about the fact of sharing my husband with someone else. I even feel annoyed when my husband teases me about angels of Jannat? Why has Allah put this feeling in us knowing the natural tendency of males? 

2. Though I know that there is nothing wrong in having more than one wife but I still feel uncomfortable and jealous about this fact. I would never be able to stand the fact of my husband marrying someone else. Does that mean that I am not a good believer as my husband constantly keeps saying that if I cannot tolerate the fact of my husband having another wife (suppose) then I am not a good muslimah. Is that so?

Authenticity of the dua for Rajab and Shabaan

Q: I would like to know whether reciting the following famous Dua is Sunnah/Permissible/Bidah:

اللَّهُمَّ بَارِكْ لَنَا فِي رَجَبٍ وَشَعْبَانَ، وَبَلِّغْنَا شَهْرَ رَمَضَانَ

Is there a strong command or a sign of permission from Rasulullah Sallallahu Alaihi Wa Sallam regarding the recitation of this Dua in the months of Rajab and Shabaan?