1) Is Dua e Nudbah Authentic?
2) I have heard that it has a weak narration chain but we can still recite it ??
3) What’s the evidence for its authenticity ?

Yes it’s authentic.
These are the references:
1. Kitab al-Mazar Al-kabeer by Jafar Mashhadi
2. Kitab Al-Mazar Al-Kabeer by Allama Tabrasi
3. Al-misba Al-Zahir by Ibn Tawus

Allama majlisi also narrated from the above 3 books.

The three books reported from the Nuwwabs of the 12th Imam.

There is nothing wrong with Dua Nudbah