1. Many sole traders (from plumbers to market stallholders) use their personal bank accounts for business purposes. It's not ideal but it's not illegal.
2. It's entirely at the discretion of individual wholesaler as to who they'll let purchase from them. However, in order to keep on the right side of the manufacturers who supply them with goods, most will insist upon seeing evidence that you're a bona fide trader. The easiest way to prove that you are (without showing them bank statements clearly relating to the business) is probably by showing them the paperwork that HMRC send back when you register your business with the tax man (which is a legal requirement).
3. While eBay owns PayPal, they still operate as separate businesses. . (You can use either one of them without using the other). So they both need to make their own profits. So, if you use a combination of their services, they'll both take a cut.
There's lots of information here:
http://pages.ebay.co....nesscentre/index.html
Chris