It would be dependent on the legal system, for example in the UK (and I presume most western countries), the adoptive parent(s) are the legal parents and the adoption cannot be voided, even in cases where children have been wrongfully taken from their parents by the state, the courts recognise the adoption (UK). Therefore your aunt would not lose custody and if she has a partner named as the adoptive father, his rights would not be voided. Your niece would have no claim to the child regardless of any right the birth father may have which, is likely to be none. This is provided the adoption was carried out legally and officially, otherwise it is likely to be much more complicated.
As for a DNA test, if your aunt is the legal parent it is probable that it would depend on her saying it can go ahead, I'm not sure how many courts would be willing to demand a DNA test against the legal parents will where there is no suspicion of kidnapping etc. If your aunt has adopted the baby legally, then she is the mother according to the law and this cannot be voided or overturned unless she puts the child up for adoption. At worst, the baby's dad (if there is no adoptive father) might be allowed access but he would not be able to take the child away and the courts would make that decision. Your niece would have no rights whatsoever as she signed them away, even in the event her ex had rights recognised in law, provided any cool off periods have lapsed ( for a newborn it usually varies from 6 weeks to 6 months once that has lapsed it is irrevocable). If the ex suspected the baby was his and did not register his objection at the time of adoption (to the courts etc) despite being aware of the process then it is likely to count against him.
So long as your aunt has the adoption papers signed and recognised by the court etc the odds are the adoption will not be voided, but should clarify with the laws in her country or state.