Is the Nikon SB-25 a 35 mm camera with manual operations?

And where can I get film and photo paper for it?

A Nikon SB25 is a flash unit, not a camera.

http://www.althephoto.com

This is a flash unit that slides onto the hot-shoe on a Nikon 35mm camera.
You can get 35mm film at places like Walmart. You don't need photo paper.

Photo class?

AS mentioned, the SB-25 is a flash unit, not a camera. Keep looking. You are looking for something like a Nikon F, F2, F3, or numerous other models. All are 35mm film bodies.

Walmart is as good a place as any for film. They carry "photo paper" for printers, but not for a darkroom. I assume you actually want the kind that gets developed in the darkroom? You will either need an actual photo supply shop, or purchase it on line from a place like B&H Photo.