You can't actually mount the 18-55mm lens on a full-frame Canon camera as it's an EF-s lens (not EF) so it's designed to physically not fit. The focal length of a lens is independent of the sensor size (a 50mm lens is a 50mm lens regardless of what camera it's mounted on) however the field of view (how wide the lens appears) will be affected by the crop, so the 18mm lens will be the same field of view as a 28.8mm lens on a full frame camera.
Incidentally I've had very good results mounting the £80 50mm f/1.8 on a £1000 Canon 5D. A lens doesn't have to be expensive to give good results if used in the right way.
Because focusing distance is the characteristics of the lens, NOT of the lens + sensor size. Lens are provided with optical characteristics which has nothing in common with sensor, mount type and so on. You need to multiply on the crop factor because of sensor size.
And yes, your 18mm on sensor with crop factor 1.6 will become 28.8mm.