Hi Kostas,
Since you provided log-in details, I did a basic configuration for you:
– First, I have disabled the default items displaying there on the Frontend search settings -> General panel: http://i.imgur.com/pn7Er3o.png
– Then on the Categories & Taxonomy terms panel I’ve choosen to display all product categories: http://i.imgur.com/5CVmX8d.png
– ..and I also noticed that you don’t have the “product” custom post type selected, but I guess you want a product search, so I did that as well on the General Options -> Sources panel: http://i.imgur.com/j8SBWDl.png
For more information on what I did, you can check the following chapters in the documentation:
– Search in custom post types
– Category and Taxonomy Term filters