There are two NO answers there.
No, you do not declare the payments as income on your return. It is not income. It is roommates sharing expenses.
No, he cannot deduct those payments to offset the rental income he must claim on his tax return. That is not an expense related to the rental income.
If this situation is prompted because you live in a state that grants a renters credit or deduction, on the state tax return (https://hotpads.com/blog/6-potential-tax-deductions-renters/), you will have to carefully review your state's rules to see if he qualifies (I doubt that he does)
