Aw, you have a tenderhearted son! How precious. I think you are handling things well, so long as you are not yelling at him (which it doesn't sound like you are). Correct him, show him by your displeasure that he is wrong. But, also, reassure him of your love. When he says he is sorry, put a huge smile on your face and tell him your forgive him. Hug him and let him know that your relationship is fully restored. Also, I wouldn't send him to his room. I think that is a huge mistake that most parents make. It teaches the children to get along just fine without Mom and Dad. It hardens their hearts against us. It does not instill an urgency at restoration and repentance from their disobedience. As they get older, they take that opportunity to stew and develop very negative feelings towards their parents. And, as a teenager, often, feelings rule the day. Instead, get into the habit of dealing with the situation immediately with your child. Start teaching self-control. I allow my children to cry for a short amount of time. After the initial tears, they find that they can get sympathy and wallow in self-pity. This is a bad thing for them. It takes time, and is an effort, but it is well worth it to train this response out of them. Be gentle. loving, but firm. Do not ever discipline in anger, but in love. Sounds like you are on the right track with your son though.
Oh, and the language thing is totally normal! Don't worry about that. Sounds like you are doing it right in that regard!