This is my opinion also. I do not see a problem with taking 6 classes rather than 7. Also, being a tutor is a good EC. This requires a strong understanding of the material that you are teaching, and shows patience and commitment and the ability to work with others. Also, university admissions understand that some people need to have a job because their family needs (or at least could use) the money.
I doubt that they would. I do wonder however: Does your guidance counselor know that you tutor younger students?