Question about marriage - non muslim woman, beliefs and ettiquitte in the modern

Salam brothers and sisters.
This is just a question that I would love to know more about and I am learning, Alhamdulillah. I am not wanting personal opinions but rather the answers to the questions being put here.

Whilst I know it is preferred for a Muslim man to marry a Muslim woman who is chaste, the Quran also has stated that the Muslim man can marry a woman of the book who is also chaste.

One question at this point I have is -
- how is this possible, for instance a Christian woman, who maybe chaste but believes that their God is not Allah or more specifically believes in Jesus?
- What if the woman is non chaste? She must repent her sins and mean it but would she have to repent as a Muslim or non Muslim? And to whom must she repent to?

For non Muslim and non chaste women who repent her sins, what is the conduct when it comes to things like aiming for marriage? Obviously, no sleeping together or living together but are you able to see them and make them feel comfortable given that they are not Muslim (yet)? For instance maybe doing social activities such as going to the movies or dinner provided that you do not kiss or do any form of adultery? But just casual conversations and activities (like playing pool/snooker or taking a walk in public parks and such)? This would solely be to get to know each other better but also to make them see and understand your faith (Islam) without being overwhelmed or judged or pressured but making them feel comfortable in their environment/surroundings.

Of course, one thinks that these days there are hardly any non Muslim and non chaste women around (which is one of many reasons to marry and aim for a Muslim woman of course!).

Thank you for your valuable time and answers. I am really interested to know the ins and outs of this.