Is a 50mm lens considered normal if using a 35mm camera?

Yes, when using a 35mm format film, the 50mm prime lens is considered a "normal" or "natural view" lens.

This does not hold true when using a Digital SLR camera (DSLR) because the sensor for most cameras is not 35mm size (36 by 24mm). Entry level and enthusiast level DSLRs often have sensors that are about half size (18 mm wide) and therefore the 50mm lens is equivalent to a slight zoom. A 35mm or 28mm prime lens is closer to that natural view.

Some of the more expensive DSLR cameras have a full size sensor and thus have the same magnification and characteristics of the 35mm film camera.