What is a fair salary for a live in caregiver?

True about the living expenses but no one should be responsible for someone 24/7 with no time off if not related. This is slavery.

In that "living expenses" you need to remember that they are providing for your entire family of four.

I suggest you type up an agreement going forward. You should consider salary, vacation, retirement and healthcare just as any employee/employer would. Assume you also prepare meals and do housekeeping, laundry. Additionally, as you state -- you will have to pay rent and bills. So consider all.

The going rate for live-in caregiver in northern va is "$20-25/hour". That is a lot.
I would negotiate if you are doing all above for a written salary of "$3000/month". You then pay your own healthcare and retirement out of that. You additionally request 2 weeks paid vacation/year -- whereby another caregiver or family member pitches in to watch over lady while you vacation.
Lastly, lady includes your living in the house (as part of this annual salary) for as long as you are caregiver. If you consider that living in the house and expenses is probably worth $1000-2000/mo depending on where you are located -- that brings your total compensation to about $48,000+.

A fair weekly salary would then be $700/week with 2 weeks paid vacation included.