If the listing is current and indexed, you can search by item number by entering the number directly into the search bar.

You can search for Sellers via the Advanced link to the right of the eBay Search window. Scroll down to the Seller section and enter the ID and complete the Search at the top or bottom of the page.

You'll see items you bought in the last 60 days when you go to your purchase history. To see older items you've bought, you can change the date range displayed. Go to See orders from at the top of your purchase history and choose the year from the dropdown.