Haraam relationship with a non-Muslim

Q: I have a non Muslim female friend. I want her to come to Islam and become a Muslim. For this I always make dua for her and show my best character (akhlaaq) to her. But when I talk about religion she tells me she doesn't believe in any religion but she believes in Almighty God that He is One. She is engaged in bad habits such as: cigarettes, wine, boy friend relationships, etc. When I told her to leave these things she got irritated and told me don't interfere in my life. I have my own life. What I want I will do. I don't care whether it is good or bad. Please tell me in this situation what should I do?

TV and pictures of animate objects

Q: If somebody tries to make me watch TV or show me a picture on their phone then what would be a wise response I could memorize?

"Many readers may not be aware that some ingredients of fizzy drinks such as Pepsi Cola, Coca-Cola and others have been dissolved in alcohol." Dr Muhammad ‘Ali al-Baarr says in his book al-Khamr bayna at-Tibb wa’l-Fiqh so is it out of taqwa these drinks are avoided? or are they permissible? Please explain how they become taahir if alcohol is used in case I need to explain to others.

Observing purdah from na mahrams

Q:

1. My mahram doesn't wear a hijaab and when she comes to stay at our home, my male relative (she is also his mahram) brings her to and fro from her house to our house and back in his car. She has been advised to wear the hijaab, but she is a jaahil who does not practise Islaam, but a little. Is it haraam for my male relative to pick her up without hijaab and to drop her off home without hijaab? My gut feeling is it is, but I would like a ruling. Does he share in her sin?

2. My mahram relatives would like me to visit more, but the problem is, in their house are women non-Mahram to me, who don't strictly follow Islaam, they free mix and don't observe purdah from me and I worry they would try to greet me physically, hug, kiss etc. So if I have fear and feel that I am weak and not confident that I can avoid this haraam then I should not attend, correct?

3. Does this count as 'severing relations'? Of course, if my mahrams comes here, I am not rude to them etc. We're fine. Is there anything such as 'severing relations' when it comes to non-mahrams like cousins etc?