unemployment insurance tax and age?

Unemployment taxes are a payroll tax. They are assessed based upon payroll, not the age of the employee. Whether he would ever file for unemployment benefits is irrelevant. Therefore you absolutely must report his wages and pay the relevant UI tax.

FWIW, most states don't bar Social Security recipients from claiming unemployment benefits as long as the employee is otherwise eligible for UI benefits. A person collecting Social Security Retirement or Survivors benefits would generally be eligible for UI benefits as long as they lost their job through no fault of their own, were actively seeking work, and were ready and able to accept an immediate offer of appropriate full-time work. Their benefits *may* be reduced slightly based upon how much their wages in their base period affected their Social Security benefits. In most cases the impact is pocket change.

The only time that eligibility for UI comes in to play is when the individual is collecting Social Security Disability benefits. Since an inability to work is a requirement to qualify for SSDI, most beneficiaries would not be eligible for UI benefits concurrently.

you might check this question with your state but I am not aware of any age limitations to the Unemployment insurance you as an employer is required to pay

now in the case of some states that the employee pays his unemployment insurance, if there is any, there might be a choice

You must include all employees according the rules of your state, which vary

in ILL, for example you cannot collect SS and Unemployment