No, California community property laws do not apply to child support. The biological parents of a child/children are the only ones who can be held legally responsible for financial support.
Yes, it is a requirement to include the income in a request for a modification. see links below.
In California, 20% of a second spouse or S/O income cane be used.
No, only the parents pay for their child, no one else.
20% can be applied. see links
In general, (re)marriage should not increase or decrease one's child support obligation, regardless of the new spouse's income or the presence of stepchildren.
That cannot be done in any state, but in California, 20% of the income of your new spouse/SO can be used in a child support modification. see link
20% in California, or through a rebuttable presumption argument in other states. see link
No, only the income of the biological parents are used to figure how much child support will be paid. Medical support does not use a spouses income either.
Not pay the child support, but under certain circumstances, 20% of your income can be used in a modification. This also applies if you are cohabiting. see link
The income of your ex-spouse's partner is irrelevant to child support; only your ex-spouses income counts.