The products will list on this page by ascending order based on the id, so the last added products will show last in the list. To update this you just need to go the the line that has the recordset on in and change the ASC at the end to be DESC.
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change from this:
ProductID) = ProductID ORDER BY products.ProductName ASC";
ProductID) = ProductID ORDER BY products.ProductName DESC";
As for the search it should be using keyword searches using like, so if you type in the partial name of a product it should return any product that has that partial term in it. Do you have a link to your site and a test search value so we can see this?