Yes, ebay holds financial information - how else do you think it debits seller fees?
Yes, indeed. If you're a seller who isn't a "casual seller", or an eBay store owner, eBay require you to put on record, account or CC details to enable them to take funds from that account or CC when you owe them money for sales.
I was a seller on eBay and when I sold then monies went in to my PayPal account and come the end of each month eBay had a, so to speak, direct debit arrangement with my PayPal account to take any listing fees and/or seller fees from my PayPal account.
My card and bank account details were only ever registered with PayPal and never with eBay!