If you have custody of the child(ren), and if the father lives in the US, then yes, you can get child support even if he's not a US citizen. If he was ordered by the courts to pay child support and refuses to pay, you can sue him for non payment. They may even order (or you can request) the child support payments to go through the Child Support Enforcement Agency, who will then forward the payments to you. If he fails to pay, then they will take legal action on your behalf.
But if he lives in Another Country, then it may be extremely difficult, if not impossible, to force him to pay the child support unless he lives in a country which signed the Hague Treaty, which provides enforcement for foreigners to pay child support.
Yes, a mother South Africa can get an arrest warrant for a father living in another country if he stops paying for child support.
Yes, he will be treated as "US Citizen born abroad"
You must be a citizen of that country, qualify through a mother, father or grandparent, or have gained citizenship in that country with out playing for another country at full international level.
no
There is nothing that would stop him. She is not a citizen of the US.
It goes by your state guidelines. see links below
It depend where you live in the world , the Law are differant from country to another .
Yes, you are a citizen by the mere virtue that your father is an American and you have lived in the country for more than 3 years.
No. Not even marriage to the father grants gives you citizenship. You have to apply for naturalization.
yes
yes
No, there does not seem to be any evidence that President Obama's biological father became a U.S. citizen, and in fact, he ultimately returned to his country.