Minor self employment tax and income

My 15yo son gets a regular, about $200/mon cash income from doing chores and yard work for neighbors.  He doesn't get a W2.

Is he considered self-employed by IRS and has "earned income"? 

What are the taxes he has to pay and how to pay his taxes (income, self-employed, ...etc)?

How to prove he has "earned income" so he can put some of that cash into a custodial Roth IRA account with him as the beneficiary?