You typically want slightly smaller eCommerce sites, and some prepaid cards have no address attached so if it comes down to a company or supplier only sending to the address on the card, you will be fine.
It's totally possible, but order once or twice for yourself (no worries, you can always sell the items you are purchasing on eBay) - you want someone that is located within the major consumer countries.
Typically, you want to be able to purchase something for 3 times less than you can sell it for, so if something is $5, you want to be able to sell it for $15, unfortunately it is unlikely you will have this kind of profit margin. Onlines stores often face a lot of competition from eBay, so you need to look for something with reasonably low prices, and free shipping. "Free Shipping" is your bread and butter, because that is where your profit will likely come from. Say a website is selling a Box Fan for $19.99, free shipping. You will want to go on eBay and try to sell it for either $19.99 + $6.99 shipping, or something like $24.99 + $6.99 shipping. So your profit will be either the $6.99 or the 4.99+$6.99. The first one will actually give you a profit of $3.48 and the second will give you the price of $7.88. One big advantage is that it isn't much to have 1000, or even 2000 items listed. Most other things will be a disadvantage to you, you will end up selling something that your supplier does not have in stock and this really pisses off eBay buyers. Your DSR's will slowly get you removed from the site as eBay has pretty much designed DSR's that way when it comes to charging for shipping. Another main disadvantage is, once you hit gross sales of $60k a year (which is Nothing, I hit that this summer selling garage sale items and auction items for a study I'm doing with students) eBay will call you up. You even mention dropshipping, you won't be on eBay long. You'll find your PayPal limited pretty quickly. At this point is where they start doing more research on you. Long story short, eBay does not like dropshippers no matter what anyone else says.
Take what little profit you can gather up, invest it into real inventory.