(1) A person in one state is declared to be liable for the support of the person's spouse, in conformity with the support laws of this state, and for the support of any child or children of his under 18 years of age and residing or found in the same state or in another state having substantially similar or reciprocal laws; and, if the person is possessed of sufficient means or is able to earn such means, he may be required to pay for this support a fair and reasonable sum according to his means, as may be determined by the court having jurisdiction of the respondent in a proceeding instituted under this article. Notwithstanding the fact that either spouse has obtained in any state or county a final decree of divorce or separation from the other spouse or a decree dissolving their marriage, the obligor under this Code section shall be deemed legally liable for the support under this article of any dependent child of the marriage, whether or not there has been an award of alimony or support for the child or children;

(2) The parents in one state are declared to be severally liable for the support of a child 18 years of age or older, residing or found in the same state or in another state having substantially similar or reciprocal laws, whenever the child is unable to maintain himself and is likely to become a public charge;

(3) A child or children born of parents who, at any time prior or subsequent to the birth of the child, have entered into a civil or religious marriage ceremony shall be deemed the legitimate child or children of both parents, regardless of the validity of the marriage;

(4) A child or children born to parents who held or hold themselves out as husband and wife by virtue of a common-law marriage recognized as valid by the laws of the initiating state and of the responding state shall be deemed the legitimate child or children of both parents;

(5) A common-law marriage recognized as valid by the laws of the initiating state and of the responding state shall be deemed to be a valid marriage for purposes of this article;

(6) Whenever a person has been adjudicated by a court of competent jurisdiction as the parent of a child born out of wedlock, the person shall be legally liable for the support of the child in the same manner in which the person would owe the duty of support if the child were a legitimate child.