I noticed that when I zoom in and out, even when I have everything in manual, the exposure changes in steps at different focal lengths. (...) since the lens is 18-200mm and the aperture goes from 3.5 to 5.6 (...) I set it to 5.6 and I zoomed in and out, but it still does the same thing. (...) Is this normal, is it because of the camera or this particular lens? In that case, is there any other lens (that is not to expensive) that will keep the same exposure at all focal lengths as long as the aperture is set manually to the lowest level?
So first off, glad you got the camera decision sorted out.
Secondly, yes, that's normal for that lens--any variable aperture lens, actually--and unfortunately, constant aperture zoom (video) lenses are very expensive, and even then, they usually cover a much shorter zoom range. e.g. Canon's CN-E30-300mm (which is constant T2.95 from 30-240mm) is $45,000.
And finally, although further Olympus and/or Panasonic questions/discussions should probably be posted in the appropriate subforum, since you asked here:
So you can put that Olympus 45mm f1.8 on the GH2 and it will work with all its functions including AF?