Can I just state this to you. There is no such thing as Extremist muslim, religous muslim, relaxed muslim, moderate muslim or as you put it, modern muslims. There's only just muslims.
The open minded muslim is a still a muslim who followed their religion. You're urged to question the religion in Islam. Why do you think so many muslims know so much about their religion? Because they ask question and find out about it.
The simple fact is, your mother and fathers marriage was illegitimate under Islam. All muslims marry according to Islam. If your dad was not a muslim, then the marriage was not a marriage under Islam and sorry to say this, but you were born out of wedlock. Under civil law and the laws of the country, it might have been a marriage. But under Islam, it wasn't. Which is why I said, it was no different to a boyfriend/girlfriend relationship.
It does matter what religion the spouse is. A muslim cannot marry a hindu, man or woman. It's important you try and understand this. There's no ifs or buts about it. Islam only allows a muslim man to marry a Jewish or Christian woman who are practising and believe in their religion. Why? Because they are referred to as the people of the book in the Quran. A muslim woman cannot marry a Jewish or Christan man. Furthermore, Islam requires that under the condition of the marriage, the Jewish or Christian mother must agree that the child will be raised as a muslim.
What do you mean you follow the rules of Islam, but not so deep? What do you mean by that? Seriously, you could you please tell me what you mean by that?
Do you follow the 5 pillars of Islam? Do you believe in the Quran?