Glenn, the problem with the first shot is not with the camera or the lens, it's with the filter. Polarizers work by blocking light that has been refracted or reflected at a particular angle. The light emanating from a blue sky has been refracted by the atmosphere, so it's polarized. (Biggest polarization effect in a ring 90 degrees around the sun, none at all for light streaming directly from the sun.) By rotating the lens you can match the angle of the lens to the angle of polarization of the light from the sky, and get as much or as little darkening of the sky as you want. It's like having an infinite variety of stops of neutral-density filters, all in one filter. (Plus, a polarizer can reduce reflections and glare in the foreground but won't have much other effect on most foreground objects, whereas a graduated filter might have to be carefully positioned to avoid darkening a foreground object.)
Given how polarizers work, it's just about impossible to shoot a panorama through a polarizer and not get that banding effect in the sky when the sun is low: once your field of view extends beyond, I don't know, thirty degrees or so, you're looking at different parts of the sky, with light polarized in different amounts. (If the sun is directly overhead, no problem: polarization occurs in a ring around the horizon.)
The solution for a shot like your first one is to use a graduated neutral-density filter instead: darken the whole sky evenly and leave the foreground mostly untouched. Or, take two different exposures and combine them digitally.
The lens cap warning just has to do with the design of the metal ring around the filter. There's no real reason the ring couldn't be extended forward to accommodate a lens cap, but filter makers often don't bother. (Well, actually there is a reason: if you put a long enough tube (filter mount + extended ring + maybe other filters) at the end of a lens, you might get vignetting aka "tunnel effect": the corners of the image darken. )
