I am a Legal Permanent Resident (Green Card). I applied for I-130 for my wife on May 20, 2016. She is here in United States as a Student(F-1) and is maintaining her status.
The priority dates got current from this October 2017.

I received a confirmation from NVC, they said that my case has been transferred from USCIS to National Visa Center and they will be taking care after this.

My question here is

1. I being a green card holder, can I file Adjustment of Status for my wife? (I-485)

2. I talked with the NVC agent, they said that after all the process completes, her status will be changed and she has to go back to the native country to get her visa.

How should I proceed so adjustment of status of the status can be done in United States? I appreciate any information on this case.

So your wifes PD is current per Dates for Filing table, so just file AOS package(i485, EAD, AP) to the USCIS and ignore NVC process. Just tell NVC that she will be doing AOS and not the visa processing. She will get GC only when her PD becomes current per Final Action table. No need to go to your native country for visa.