What will I have to do to become a background dancer? Is this a good plan?

Kathryn is correct. Her answer has my thumbs up. Backup dancers are classically trained as well as doing street jazz and hip hop. They must be able to do anything the choreographer wants them to do. Anything less than 15 hours of technique classes a week (rehearsals and learning a dance aren't technique classes) is considered recreational training. It is really hard to get work and only the best of the best get work and not all of them can make a living at it too. You should also know that running reduces flexibility and bulks your leg muscles instead of elongating them to give you a good line in dance. You have missed a large chunk of one of the most critical times in your dance training. Form age 11-15 when your body is changing, is a key time to train those muscles as you grow.

I am not saying that you cannot do this, but stop the running in favor of other cardio like walking or swimming. Take lots of ballet classes even though you don't want to dance ballet. It is important in building body control and technique. You may also want to add pilates to elongate your muscles, build strength in your core and increase your flexibility if you have the time or cannot take daily ballet classes. You will realistically have to take 5 or 6 days a week of technique class to be competitive and multiple classes a day. My daughter has a friend who she trained with in high school, who danced backup for Janet Jackson. She was ballet academy and Graham & Horton modern trained. She studies at Alvin Ailey and was a dance major at LaGuardia H.S. Not to mention she came in 4th on SYTYCD.

Like my daughter, she took 20-30 hours of technique classes a week. It is really hard to hav a career in dance.

Sorry to say this, but you actually don't have a lot of time. You are already behind in training compared to most girls your age with the same dream. You'll have to do one hell of a lot of training to help you catch up, and let's hope you have talent or you'll never excel. Dance is such a competitive career that doesn't last more than 10 to 15 years for most people, for little money and little fame. I would recommend, if you are serious about this, to dedicate all your time and effort into dance lessons right away, which will be difficult alongside school, but you can manage it, and don't drop out of your educational studies, you'll need them when your dance career fizzles out, because I can guarantee you probably wont still be dancing when you are 40, and almost definitely wont be when you are fifty, but you'll still need to pay those bills. Just being realistic, thought it was fair for you to know your chances.

You relatively must be taking as many categories as viable every week (20-30 hours if viable). If you wish to do cutting-edge I might consciousness my power on ballet and cutting-edge, the opposite categories I might hold however I might up the quantity of categories within the two patterns I acknowledged.

Backup dancer?! Wth! Be a choreographer, run your own ish!