If I am paying someone to stay with my Father, do I deduct taxes?

If you are paying the caregiver directly, yes, you should. The nursing home may have a service you could pay instead. I'd look at that route. I would tell you that you are unlikely to get caught if you just pay a person directly, but, frankly, if you just pay them directly, it's not the IRS you have to worry about.

How about asking the doc to prescribe sleeping pills for him?