Is a non-biological parent legally finically responsible for the child? Does visitation right exist?

You really need to get an attorney. It would be in the children's best interest.

Yes, you do need help and your question is too complex for this forum and the jurisdiction where you and the children reside will have potential effect. See an attorney. Generally if there is no biological relationship there are no parenting rights. However, in this case, due to the passage of time and the previous payment of support there is a possibility you might prevail.

Biology is only one way to be recognized as the father of a child. A "presumed father" refers to an individual whom the law presumes, until shown otherwise, to be the legal father of a child. A presumed father may not be the actual biological father of the child. A presumed father can be a married man who is married to the mother when the child was conceived or born; an individual who has legally agreed to be the father of his wife's child, or has acted and behaved as if the child was his own. I advise you to seek help from a family law attorney in your area. It seems you may need to solidify dad's rights with a parentage action and an order defining custodial rights. All parents have an obligation to financially support their children.

He has held the kids out as his own and raised them. He may well have rights. See an attorney about filing for custody.

If the child was born during the previous marriage, and if divorced, the father is presumed to be the biological father. If paternity was not contested during the divorce, then it is too late to do so now.

You folks have some rights, but the Court is mostly concerned with the best interest of the child. Wisconsin appellate courts have held that if a child has been raised for years in the belief, shared by his or her father, that they are truly parent-and-child, even if DNA evidence shows that the father is not the biological father, he can still be required to pay support. More to the point, if you have been raising this child for almost all his life, I assume that you and he have formed bonds of affection which would hurt all of you to break. There is provision in the law for a non-parent who has a parent-like relationship with a child to sue for 'visitation,' that is, some periods of placement. Another option is to consider filing a paternity action in which the non-biological father asserts he is the child's father, and let the mother go to the trouble, if she wishes, to contest it. Your rights are not as strong as you might wish, but you do have some. You really should consult a lawyer. Good luck.

If your husband is not the bio-logical father and there has never been any court order concerning custody of the children, he has absolutely no legal rights concerning the children, except the right to seek legal custody based on the fact that he apparently been actually caring for the children for some time and the actual parents have more or less abandoned them. So, until he files a lawsuit and obtains specific rights from a court, he has no other enforceable rights. He needs to immediately contact a lawyer to discuss his options and how to proceed to obtain a judicial determination of what is best for the children. Generally, he has no legal financial obligation beyond what he has voluntarily assumed by raising the children and the mother's demands come close to illegally selling children.