Nikaah & Marriage Issues

Marrying a girl who was engaged to one's cousin

Q: There is a girl whom my cousin was previously in love with. The whole family knew and since he was still studying, the family wanted to marry them once my cousin's studies were over. After a year, for some family reasons, my cousin left the girl. I know that girl and I want to  marry her and she too wants the same. When my parents and the girl's parent came to know about this, they are telling us that this is not possible, my cousin won't like it, what other people will say, what elders will say etc. In my point of view, its more society and culture thinking. I wanted to know what Islam says about this? What is the view?

Choosing a spouse

Q: I am 28 year old. I have been fairly successful in my career and I have never been married. I am very well groomed and have chosen to remain pure out of the fear for Allah Ta'ala. I will prefer to marry a muslim women with similar traits in compliant with Shariah. I am well versed in the Qur'an. Should I find a women around here and just marry her or will it be permissible for me to ask a Mufti to refer good muslim women for me to choose from, as I want to do it according Shariah strictly. 

Ijaab and Qabool in the presence of witnesses

Q:

1. If a proposal and acceptance take place between a man or woman so are they married. Is this valid or legal in shariah.

Once in a TV program I heard that if a Muslim man and woman accept their proposal and accept each other then they are married and nikah takes place even if no one is present in between them. He said that this is called Nikah Ijaab and Qabool. Ss this true?

2. I also heard that for nikah Ijaab and Qabool​ permission, wish or willing of a woman's father is necessary.

3. If a man and woman accept each other in the presence of her mother and her 14 years old brother, so in this case nikah takes place or not?

4. If a father of a woman wishes to marry her daughter with his sister son (Nephew) and both the girl and boy are fiancee and fiance and both the parents wish to marry them but both girl and boy accept each other saying nikah words in the absence of any witness and both parents are also not present at that time so in this case nikaah takes place or not?

Non-Muslim changing his name

Q: My friend has recently reverted to Islam and the question has been asked if he has to change his name or he can keep his name?

Also, he is soon to be married, Insha Allah, to a Muslim girl... if it is permissible to keep his name, does it impact the performance of the nikkah in any way?... Can the nikkah continue as normal with just his non-Arabic name?