If you are talking about the shopping cart itself, after folks put stuff in it: I would make that a noindex. I get paranoid about security and privacy so I would keep anything that is personalized in any way out of the search index. You don't want a link to a shopping cart with specific shopper id to get into Google. Even if the shopper id doesn't tie back to any personal data, you could have multiple people with the same cart id.

Anyway... I would suggest making the cart a noindex... I'm paranoid about it so I'd play it safe.

You can have canonical from one domain to another.

I am talking about have the ability to actually control eBay's meta data at the canonical level. They already have canonical tags going back to their own pages and I doubt they would give you control over it. Again, I am not 100% sure but I would be shocked if they gave you control of that field. eBay has its own SEO concerns so I image they would retain control of that field.

I just don't consider a product page on eBay to be a duplicate of a product page on a third party site even if the site were feeding the data to eBay. Your site and eBay are 2 totally separate entities and I don't think these would be considered duplicate pages.

I don't think it would be too bad. A cleaner name would be better but having the new images show is important too. More important in my opinion.

We use an RSS feed for new product lists. We may have some lag time before a new product gets put in a category and able to be browsed to on our site. The RSS feed gives a few days head start getting these new products into the search engines. We redirect all RSS links back to the main site links that include canonical tags for the main product pages.

Google may have the images cached and not realize you have new ones. One rule of thumb I try to promote is to always use unique image names. You may find your customers also see old images if an image of the same name already resides in the browser cache. I encourage our marketing folks to add a date stamp to the end of an image so it will be seen as new. Versioning will work as well.