Yes, yes and yes. Distance only makes the perspective. The focal length and the sensor size determine the framing for a given distance from a subject.
My 8-15 and 200 have the same perspective? If I cropped the 8-15 to the same framing of the 200 it's the same perspective?
An ef 35mm lens on a on a crop is not the same perspective as a 56mm on full frame.
As to the focal length equivalents: It is really a function of the sensor size, not of the lens. EF or EF-S doesn't matter. People/companies talk about the equivalent length to be able to compare how a lens on a certain camera feels in regards to the FOV, but they should really do so when talking about the camera, not the lens.