Do I need to register a business?

[tro]

there is a misconception about 'registering' a business
first your local business license department may require you to get a license which will mean you may be required to publish your fictitious name in the local newspers(a DBA)
then if you plan to pay employees you are required to apply for an EIN with IRS and probably similar number with your state, this means you withhold taxes, file quarterly reports and pay what has been withheld as well as the employer's portion
if you form a partnership this will mean the application of the EIN and also indicate on that form that you will be operating as a partnership, this will require filing form 1065 annually for this business
since all this is way beyond your tender years, you would do well let each of you handle your own repair, advertise your services that you will provide but keep your income and expenses separate
if your net amount is $400 or more yes, you do need to report this income on Sch C and Sch SE with your 1040