I have been living with and taking care of my 80 yr old parents,full time, for 3 yrs. For about 6 months, mom was feeling generous and gave me $500 a month as payment. They have not charged me rent. Mom and I haven't been getting along.(understatement) She wants me to move out. She can't take care of dad,(she was recently diagnosed with dementia as well), but she wants me to go immediately. Does she have to give me a 30 day notice?

By the way, Im in California

Yes she has to give you a 30 day notice to move. But she can ask you to do that.

Yes she must give notice and evict if you do not leave voluntarily. However, it is not your fiduciary responsibility to give her legal advice. If you want to stay you can just ignor her wishes, that's all it is right now, and continue to provide care. You might explore what consitutes diminished capacity regarding your mom, this will likely continue to worsen.

Since this is CA you may be considered a lodger. Which means they don't have to go to court to evict. You still need to get notice equal to your rental period