Are Christians under the 10 commandments?
No. The Bible says we're not under the law.
I love Romans 7:4-6. By way of analogy, it says that you are married to the law. And you better stay married because if you leave this husband and go marry another you are going to be called an adulterer. But if your husband dies, then you can go and remarry.
And then Paul draws the analogy out—a little complex the way he does it—saying that you died to the law. You aren't married anymore, you can have another husband, namely Christ. He's raised from the dead.
So, our approach towards ethics is different. We don't ask the question, "Am I under the law?" We are under grace. The law is already fulfilled perfectly by Jesus. We are in Jesus and as far justification goes, God sees it as completed for you, one-hundred percent. He says, "You've trusted my Son. You've been grafted in him. You are in Christ Jesus and he fulfilled the law perfectly. He covered all your sins." God sees you in and through Christ, therefore, as far as final judgment goes God is 100% for you. That is settled and nothing is going to change it.
Now, shall we sin that grace may abound? Paul says, "Dead men don't sin." If you've died to sin, how can you still live in it? The new birth is the writing of the law on our heart so that we are not under it, it is under us. It is just coming out.
The way we strive towards being obedient, holy and loving people is not by getting up in the morning and pulling the list out of our pocket. No! We get on our knees and we open ourselves to the whole counsel of God in the Bible. We saturate and shape ourselves by everything he has done, he is doing and he will do. We stake our lives in the gospel and then instead of serving the law, we serve one another in love.
Love is the fruit of faith in Jesus—faith working through love. And if you ask, "What does love look like?" First John says, "It keeps the commandments." That brings us back to the question, which commandments? I would say, the ones that are loving.
Love God and do as you please is not bad advice, if you're bent on holiness. If you're bent on love the ten commandments are really important. You should hang them on your wall and you should measure your life by them, but in a very different way than when you were under them, because they have been kept for you.
You are now married to the risen Christ. You are not married to the law and the oldness of the letter, but to the newness of the Spirit. Our whole approach towards transformation, love and life is different than list keeping.