In California, a resident is defined by his/her "domicile" (see CA Revenue and Taxation code).
When your domicile changes to California is a matter of facts and circumstances. For example, what make a new place your "Domicile"?
It's various things, like when you got your drivers license there; when you registered to vote there; when you bought property there; when you got a utility account or landline there (if people still do that); when you notified the Post Office at your previous location to have your mail forwarded.
Most importantly, "domicile" is a matter of intent. When did you move there with the intent to live there?
As you can see, there is not a simple definition of what constitutes "domicile", and you will have different dates for different questions above.
What you have to do is pick a date and then be prepared to defend it if the state ever asks you about it.
NOTE: this is also discussed in the instructions for FTB Publication 1031, but it is not available online. You can order it at this webpage.
And as for your second question, I believe that you should be able to enter adjustments for capital gains made while a CA nonresident. In the CA interview, look for adjustments for nonresidents.
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