Here is what I was able to find:
1. Do I need to have the child fill out an I-9?
Yes, but there are special instructions for minors:
- Parent or legal guardian of a minor employee completes Section 1 and writes, "Individual under age 18" in signature space.
- Parent or legal guardian completes the Preparer and/or Translator Certification block.
- Employer enters "Individual under age 18" under List B and records the List C document the minor presents.
2. Where can I find the laws about working hours and minimum wage for minors?
Working hours:
New York State labor laws are slightly more strict than the federal:
https://www.labor.state.ny.us/workerprotection/laborstandards/workprot/nyvsfed.shtm
Minimum wage:
The Dept of Labor's Youth & Labor page states:
Occupations such as babysitting are not subject to the minimum wage law.
No supporting documentation is given.
Another page describes the Youth Minimum Wage Program:
A minimum wage of not less than $4.25 may be paid to employees under the age of 20 for their first 90 consecutive calendar days
However, I can't find any such exception in New York State minimum wage law.
3. Do I need to withhold anything from the paycheck?
According to Publication 926, Household Employer's Tax Guide:
Federal income tax withholding
No, I am not required to withhold federal income taxes from a household employee. If we both want them to be withheld, a W-4 should be submitted to me.
State income tax withholding
No, according to NYS Pub 27:
Withholding income tax (federal or New York State) from wages paid to household employees is voluntary on your part and your employee
Social security and medicare
No, I am not required to withhold FICA taxes because when calculated wages, I should not include:
An employee who is under the age of 18 at any time during the year.
Exception: Count these wages if providing household services is the
employee's principal occupation. If the employee is a student,
providing household services is not considered to be his or her
principal occupation.
Unemployment insurance
No, I don't think I have to pay federal unemployment tax. I think the exception for FICA applies to FUTA. For New York (according to Household Employers Guide for Unemployment Insurance), there is an exception for paying state unemployment insurance:
Daytime students who attend elementary or high school (However, you must pay UI taxes on wages you pay these students if you are liable under FUTA.)
4. How do I create a legitimate timesheet and paystub?
I can't find any specific requirements, but aside from numbers of hours times rate of pay, you might want to consider the information required by the Wage Theft Prevention Act:
- The employee’s rate(s) of pay
- The basis of the employee’s rate(s) of pay (e.g. by the hour, shift, day, week, salary, piece, commission, or other)
- Whether the employer intends to claim allowances as part of the minimum wage, including tip, meal, or lodging allowances, and the amount of those allowances
- The employee’s regular pay day designated by the employer in accordance with the frequency of pay requirements in the Labor Law
- The name of the employer and any "doing business as" names used by the employer
- The physical address of the employer's main office or principal place of business, and a mailing address if different
- The telephone number of the employer
- Any "such other information as the commissioner deems material and necessary"
Also, consider this requirements from the NY Minimum Wage Act
Every employer shall keep true and accurate records of hours worked by
each employee covered by an hourly minimum wage rate, the wages paid
to all employees, and such other information as the commissioner deems
material and necessary, and shall, on demand, furnish to the
commissioner or his duly authorized representative a sworn statement
of the same.