What you see there is what is commonly referred to as transparency acne. It happens because the way the effects processing engine looks for edges to apply edge fading on is to look for changes from the previous sheet. But if two overlapping pixels are the same color, that causes the effects engine to see it as no change, and therefore a spot to apply edge fade to.

The common way to work around this is to create a new sheet just below it in the sheet order with the same effects on it, then make a copy of the entity on that sheet, but change the fill to a solid color guaranteed not to appear in the textures, such as pink. You might want to make the sandwitch entity a little smaller than the actual one, to make sure you don't get a pink glow at the fading edges. You could also use a colour that is more similar, but you must be certain it's not found in either the sheet above or below.

No, that won't work, because that doesn't import the fill styles into the template. Changing style only changes which drawing tools are displayed in the dialog, but if you don't import the fill styles first, those tools won't have their fills.

The easiest way to use textures (fill styles) from another style is to first make a blank dummy map in the style containing those textures, then in your actual map, go to Draw -> Insert file and pick your dummy map and hit ok. Once you return to your map with the dummy map on your cursor ready to place, just hit escape immediately to stop placing it.

For most maps, just set the 'Restrict image to map border' option in the export options dialog, and it will take care of it. If the map is somehow missing a map border, use the rectangular section jpg file type when saving, as this will cause CC3+ to prompt you for the corners of the export before saving the image.

Yes, just hold down the control key and click on an entity to deselect it.