You can do a test any time after the 10th week of pregnancy. There are two methods; amniocentisis or CVS sampling is done after the 12th week of pregnancy, both are invasive procedures so it is...
You can only "amend" a paternity affidavit if you have a paternity test done to prove or disprove paternity... In many cases this is something that the state will do (ie of child support orders)
A paternity test can determine if there is a parent-child relationship between two people. A paternity test would give genetic proof of that relationship.