Can the checks from a disabled parent for an underage child be given directly to them. Or does an adult have to be on the check as well?

The check goes to a guardian or parent who has custody over them for their care. You can not for example set up a bank account for them yourself and send the money there.

The parent whose name is also on the check should be able to set up an account, remember in the US a minor child can not set up their own bank account but has to have a parents name on it.

What if child is living with non-related guardian?