Can I take online classes in another state?

There is a waiting period if one comes from one state, then moves to another state and goes to college. It is one year in a state before you qualify as a resident. So in the situation where you are in California, you might want to think about staying in California for a two year period, getting one's degree from a community college in California and letting your boyfriend go to Arizona to get a job. After one get a community college degree your degree in California, then you could join him in Arizona.

If that is not acceptable, the other option is for both of you to go to Arizona and both work in Arizona.for a year or two years Then after a year in residence, one might consider going to the community college in Arizona with an in-state tuition rate, get a degree and get a higher paying job because you have that degree. Good luck.

I was a college professor of education at four universities.

Yes, you can take online courses from anywhere. Some colleges have a flat rate for online courses- it doesn't matter whether you're in state or not. If you move, you won't be considered a California resident for very long- take a look to see who offers a flat rated. But the cost in Arizona doesn't sound particularly high to me. I think you need to look into sources of financial aid.