Hi!
As to backgrounds, given the issues with lint/dust, etc. that you mention, I'd stick with lighter/white backgrounds, or use the stone/hard surface you're using in some of the photos. It doesn't bother me personally to see one or two little motes of dust in pics like this, but you might try using a piece of wood or other painted material and see how that works. Taking the pics outside in natural light is good, but quite a few of them still need a bit of post-process brightening to soften any shadows from the shady area you're using.
Plus, are you sizing your photos according to the measurements Etsy uses for thumbnails, etc.? This one, for example, the necklace gets cut off in that initial thumbnail users see.
https://www.etsy.com/listing/125206950/green-pearl-and-swarovski-crystal?ref=shop_home_activeCan you zoom out slightly to give yourself more room to crop at a roomier rate so that the composition shows the entire shot of the set? There's a thread directly below this one that gives the various thumbnail sizes Etsy uses.
Other than that, for the most part I think your pics are clear, and the colors overall look good. Just a bit of editing to soften those shadows and bring out a few highlights in the pics, and resizing a few of the images, and they should pop more.
Hope this helps!