Well, classic is probably most similar to Turbo-lister, i.e. you do it at your desktop and then submit. Not my thing, so I'm doing a very simplifed comparision. I've been to the page and seen the free product (long time back).
The new site is a fully integrated over the network product (no desktop software) with one-page lister, templates, image library storage, checkout where you can use your Merchant card account, simple-Store (not ebay Store), Scrolling Gallery, Listing Scheduler, optional Shipping Insurance plan.... more like using the ebay one-page lister over the net, but with alot more features and FREE (except for insurance and anything they offer as custom build for you). Store Inventory is in beta, and full eCommerce Store is discussed by the Auctiva folks as potentially coming next fall (in time for XMAS season shoppers).
Generally, you use one method or the other but not both.
That's the quick version and probably answers question #1.
It might also give you insight into relevance of #2 and #3, as those are more specific to Classic.Most of what you probably have seen on ebay with those using the Auctiva templates and Scrolling Gallery are "NEW" site.
If you haven't yet completed getting the ebay Token on the new site, you'd best read the FAQ at HELP (top of page), as all your active listings will be pulled and updated with Auctiva embeds (like the SG)....and it takes time.
Danno