Why didn’t you discuss it with her then? You made the demand she move out, and unless she indicated otherwise you probably should have proceeded with the assumption she was going to move out. In any event, she did as you requested so I don’t see that you have much room for complaint here.
I don’t think so. The details of the living arrangement and the notice you provided matter a bit in exactly how this plays out, but in the end I think the result would be much the same. If she was your tenant then the question is whether the notice you provided met the requirements under California law. If it didn’t, then your demand was ineffective and you could not have forced her out. If it did, then you could have forced her if she failed to heed the demand.
But either way you did make the demand indicating your intent to terminate the lease, either justly or not. She left at your demand and, as I indicated earlier, you really aren’t then in a position to complain that she as you asked. This is unlike a situation where you intended the lease to continue and she abruptly left, improperly terminating the lease early.
Consider yourself lucky: you got rid of an unwanted roommate without the hassle or expense of an eviction lawsuit or even having to pester her about going. In the end that’s a better outcome for you even though you waited a month to start looking for a new roommate to replace her. If she wasn’t even really a tenant then she had contractual obligation to you to begin with and meeting your demand for ejectment was all you could expect. In any event, I think your best course of action now is to just forget her and simply move on to finding a new roommate.
The cure for not leaving keys: change the locks. You should do that even if she returned the keys to guard against the possibility she has another set of keys you do not know about.

