Is it okay for people to come in cosplay? costumes based on Japanese anime and manga? Because the setting is perfect for pictures.

Yes

Yes of course. The cost is 7 dollars per person but really well worth it.

Sure

Costumes okay. Weapons no.

It is open to the public. It all depends on what your definition of what "okay" is. Chernobyl is a perfect setting for post-apocalyptic pictures. Have you thought of cosplaying at Chernobyl? It has that same cancer inducing radiative feel as cosplay.

They may try to charge you a specialized photography fee. They may consider a costume to be a prop. Check their website for details.