This is a difficult & tricky situation. On the one hand, you want to set limits for her especially for unacceptable behaviors. On the other hand, she is becoming a young adult, and you have to respect the fact that she will be making her own decisions over time...regardless of whether they are good ones.
The main thing to do is try to establish a dialog with her. You want to know about her relationship with him. You want to know about her thoughts, feelings, and opinions on sexuality. Even if you think she should wait till she's 18 or married to have sex, she may not agree. I assume when you want to "trust them to do the right thing" you mean not having sex or going to quickly physically.
But you are not best friends, you are parent/child. This dialog can be hard to establish openly at your daughter's age...especially because it is a normal part of development for people her age to start connecting more with their peer group than their parents.
The down side of forcing a break up is that it may make things worse. She may then start to see him behind your back & lie to you about it. I think you are better off acknowledging her choices in life, but leaving certain limits. For example, they can go to dinner and see a movie, but most be back by a certain time.
Or he can come over to spend time with her in the house...where you will be in the other room (giving them some privacy but also able to keep an eye on them).
Consider offering her the chance to see a therapist if she needs an objective adult to talk to, or see one together as a family (this is good because it sends the message "Let's work on our problems & communication as a family" instead of "You are misbehaving...you have a problem...go see a professional to fix it.")
I hope this helps. Let me know if you have other questions.
There is no write or wrong answer here. In general, the punishment should fit the crime...I think between 1-3 weeks would seem fair...although keep in mind 1-3 minutes may not seem fair to her (and 1-3 weeks may seem like a lifetime to her).
On the one hand I agree with slowly approving whom she can contact, on the other hand this risks another power struggle between you guys...again it's a tricky balance of needing to avoid power struggles, and yet you still do maintain some authority...you're the parents who pay the bills...when she turns 18 and supports herself she can do as she pleases.
Another option would be to no restrict whom she can contact; if you have the ability to review her texts every week to make sure there is no inappropriate content, that would make this a better option. And you could reserve the restrictions should something else happen down the road.