Lets see if I can't answer some of these
Why does the cart not empty once items are paid for?
It shouldn't do that, I'd contact
service@shapeways.com about this.
Why are my models listed as "accepted" and then days later rejected as unprintable?
The models must go through a manual inspection. A person has to look at your model and see if it will survive printing. If they think that it won't they reject your model.
Why does it take such a long time to produce each item?
So many reasons. Order volume, the manual check, printing takes a few hours up to a day, then cleaning and any other post processing, and finally packing and shipping.
Is there any way the visual of a new model could be less -- well, flat? Could it be tilted just a bit more toward the vertical so potential buyers can see the design better?
You could rotate the model before exporting it which would make you model tilted any way you want, you can also upload your own image and set them to show first instead of the standard render
I have ordered several items that were then deemed unprintable. Of course, they were already paid for. I attempted a fix and reuploaded and reordered. How will I get credit for what I had paid for before?
You will get an email saying you order has been canceled, why it was canceled, and a refund code for you to use in your next order, for the amount of the rejected order.
How does a stranger select a material and purchase one of my models?
Same way you do, you just have to make sure you go into edit mode on your item and turn on or off any materials you do or do not want it available in.
Is there a glossary of terms of art? I don't know what a lot of these things mean in this context, which makes it rather difficult to comply.
This one, I'm not sure what you mean.
Questions are fine here, you had a wide range, but at the bottom of the forum there are sections for questions on 3D printing, design, applications, and buying. We'll always be glad to help and guide you in the right direction.