Will old K-mount lenses have the same field of view on Pentax K01? Or, will 50mm lens (made for 35mm film) function as a 75mm lens?
The lens will function as a 50mm lens. The sensor has a aps-c crop factor 1.53 sensor, which will give you a FOV as a 76.5mm lens on a 35mm sensor.
I might add that I use the k-mount pentax 50mm 1.4 on my 1.6x crop factor camera and it is a very nice and convenient combo.
The K01 has a smaller sensor than 35mm film, so the field of view is cropped.
The width and height of the sensor is about 1.5x smaller. Because of pretty simple geometry, it works out that the effect on field of view of cropping is exactly the same as zooming by that amount. So, while the lens doesn't physically change, the field of view is equivalent to that of a 75mm lens on a film camera.
Answers to What is crop factor and how does it relate to focal length? (and to other questions further linked from there) go into the technical details. There are a lot of misconceptions around "crop factor", so we're using very careful language, and you can get all the details there.