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Once she and the child have lived in California for 6 months she can then file there. While it will be a challenge to serve the father who is overseas but she can get a default order for child support if the judge allows alternate servive methods. If an order is established, then one remedy is to withhold his passport until he makes his child support payments. There is a state agency that can help with the process...http://www.childsup.ca.gov/
No it is not usually an issue. It is only the paying parent's income that is considered.
Yes I meant his income in this case.