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I's not against the law to submit job applications on behalf of other people. The only time it would be illegal is if you are filling out an application and it requires you to sign someone else's name or if it has you swear you are the person actually applying. In that case, the applicant themselves needs to do that. There are no real requirements to starting a business like this. You'd need to look into getting a business license from the Secretary of State, but that often just requires paying a fee.
Because I value your input, did you have any other questions about this that I can help out with:-)?