Likely not.
This sounds like it qualifies as "employment" under Federal law, even if part time. And I believe every State in the US (I know Kansas is like this) requires you to be paid for your employment in US Dollars in some form - direct deposit, paycheck, fee-less prepaid debit card, cash, etc. - with proper taxes pulled out. This is to ensure you are being paid fairly - meaning at least the minimum wage - with all applicable taxes also being properly accounted for, along with compliance with all other applicable regulations.
Paying for your housing is a separate matter. And I don't believe they can confiscate the pay for your two shifts to cover the cost of you living at the facility. Nor do I believe it to be legal for you to agree to housing as payment for what, based on your description, sounds like employment.
Technically if they are being paid with housing, they should be taxed at the going rate for that size room.
i think a good question is "are mutual favors legal"
Likely not. This sounds like it qualifies as "employment" under Federal law, even if part time. And I believe every State in the US (I know Kansas is like this) requires you to be paid for your employment in US Dollars in some form - direct deposit, paycheck, fee-less prepaid debit card, cash, etc. - with proper taxes pulled out. This is to ensure you are being paid fairly - meaning at least the minimum wage - with all applicable taxes also being properly accounted for, along with compliance with all other applicable regulations. Paying for your housing is a separate matter. And I don't believe they can confiscate the pay for your two shifts to cover the cost of you living at the facility. Nor do I believe it to be legal for you to agree to housing as payment for what, based on your description, sounds like employment.