why I can't see the links I added to bookmarks on Speed Dial?
Because you didn't add them to Speed Dial. 🙂
Do I need to add a website to the Favorites and to the Speed Dial to see them there?
You need to add it to the Speed Dial folder when you bookmark it for the page to appear on Speed Dial.
So, my suggestion is to add another row in the Speed Dial called "Bookmarks" where all the bookmarks are displayed
You should be able to create a bookmark folder, put your bookmarks there and then move that folder to the Speed Dial one.