Can I send an email campaign only to one customer group?

Yes, as long as those customers are also newsletter subscribers.

1. Go to Marketing → Email Campaigns and click New campaign.
2. Enter the Campaign name and Subject line.
3. In Audience, choose Subscribers in "group name".
4. Click Next: Design the email →, write the email, then Send now or Schedule.

Only people who are subscribed to your newsletter and whose customer account is in that group get it. Group members who never subscribed, or who unsubscribed, are always left out.