1) the right to pay child support; 2) the right to an order setting forth visitation
Yes he may. Age has nothing to do with paternity. If you are the child's biological father, you have the right to sign the child's birth certificate or an affidavit of parental acknowledgement.
He is recognized as the father by the state unless he petitions to have it proved otherwise
Take legal advice. Paternity has to be proved not assumed, first.
This could be called "perjury." If you want to establish that you are the father, run, don't walk, to the appropriate court and request a determination of paternity, probably by genetic testing.
It depends on the age of the adult child and the statutory limits of the state in which they live. For example, in Florida the statutory limit for establishing paternity is 18 + 4 years. The following site has more information: http://www.legalmatch.com/law-library/article/state-statute-of-limitations-to-establish-paternity.html
maybe
It depends on how you answered the paternity suit. If you are not the parent and it is proved that you are not the father, nothing more needs done. If you are the parent, many more court dates could come to determine custody and child support.
When the issue pertains to unmarried couples the law presumes the mother to have full legal custody of the child(ren). The father must establish paternity before custody, child support or visitation rights can be addressed by the court.
If the father can not sign at birth he will have to go to court to be allowed to sign after he has proved paternity.
Through a DNA paternity test.
No. I doubt you are the only one in the world with that last name. You don't own your last names unless you patented it. A unmarried father have rights to his child if he proved paternity in court. Not otherwise.
Under UK Child Support law, the CSA would order the test and if he is proved to be the father he would pay for the test after the event.