Can a spouse being full time caregiver get paid?

Nope. BUT if spouse is a wartime veteran, there is a program called Aid & Attendance that can pay for caregivers to get you some relief. And Medicaid waiver programs can send caregivers to get you some relief. If spouse is on Hospice, they have a respite program.

Yes, your husband can pay you from his savings/retirement fund. You would need to have an employment agreement in case later down the road he needs Medicaid.