If this cannot be avoided because it is your favorite scene, try to hold a paper or use your hand or a lens hood to block the incoming light. It usually partially solves this problem. This is because a polarizer is stacked on a UV filter and then zoomed out. To avoid this vignetting problem, do not stack filters on top of each other. Both types are slightly visible with on-camera zoom lens.
Barrel distortion means straight lines in real world bow outward in images.
The closer to the image edges, the worse the barrel distortion. Barrel distortion usually occurs in the wide angle side. On the other hand, pincushion distortion means straight lines in real world bow inward in images. Similar to barrel distortion, the closer to the image edge, the worse the pincushion distortion. Pincushion distortion usually occurs in the tele side.