I believe you know the answers to these questions very well.
1 - How close it should be, is dependent on the beliefs and the character of the person (even if he was a Muslim).
2 -
Do you have a link that explains that opinion in details with providing justifications?
I believe that opinion says it's not preferred to marry a non Muslim woman in a non Muslim country, the reasons could be that the Muslim there need everything that preserve his religion and that of his kids. The Muslim woman shall be more capable of doing this job.
3 - I am not sure about phrasing it this way "because Muslim women should not be under the authority of a non Muslim". The
Muslim husband is the head of the house. If we talked about a non Muslim husband the rules are going to be much different. The Muslim husband has obligations that stems from the fact that he is Muslim. The Muslim husband has the responsibility to protect his family on the physical, spiritual and emotional levels. He has to support it financially. The kids are going to have his name and his religion. How can I ask a non believer to fulfill these obligations? How can I ask him to preserve his Muslim wife's faith? What should we tell him if he wanted his kids to follow his religion or beliefs?
I'd like to quote Fullyveiled Muslimah's thoughts on this:
4- Basically if you are a good Muslim, when you choose to marry even a Muslim woman, you should choose the pious one. The prophet pbuh urged Muslims to marry the woman who is committed to her religion. Then naturally if you want to marry a woman from the people of the book, you should choose the pious one that will help you to preserve your faith and that of your children.