If you mean the eBay item number, yes you can. Click the advanced word just right of the search button. You will then have to search sold/completed items to find it.

If the listing is current and indexed, you can search by item number by entering the number directly into the search bar. Just paste your own item number of those digits at the end of the page address. That will work even if the listing has ended within ninety days or if it is not yet indexed.

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.