I am working H1B (in CA), my spouse is F1 and we live in different states (in NJ). My son lives with her. They live in NJ throughout the year and just comes to visit. I provide support for my son.

Can I file my son as my dependent? Or as F1 can my wife file him as her dependent?

Can my wife file as resident for tax purposes since she has been here for a while? If so, can we file as married filing jointly or separately?

In the last year, we filed married filing jointly (federal) and filed married filing separately (state). However, California has issued a tax claim for unpaid taxes due from wife's earning. Can you please elaborate on this? Can California legally tax my wife even if she's not a "resident" of California?

If she does file for tax as a resident, will her immigration status be affected?

You should file joint return for federal as well as for the state. For CA, you are resident and will report your income. Your spouse is nonresident and does not have any CA income.

About CA tax bill, you should reply that your wife never worked in CA (if it is true) and attach NJ tax return.

If she is considered resident of CA, then she will also report worldwide income to CA and claim credit for taxes paid to NJ. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)