I like your idea of billing on a monthly basis. It makes renewal discussions less frequent, especially if you have them on auto-pay. Then, if they’re blowing you off, you still get paid.
For most of my in-home clients, I have a 24-hour cancellation policy and I will give them one warning before I start charging them. I have one client I’ve treated differently because her travel and work schedule are not completely under her control, so I have a more flexible policy with her, but she also pays me a bit more.