@Fermin: Please post in your site URL so that I can check in and better server you.
1.- move the text of menu to the center.
— There are different menu is Catch Evolution Pro theme. So, which menu are you talking about. Also the menu text is align center. I think you are talking about moving the primary menu in center. Then you can try adding in the following css in “Appearance => Theme Options => Custom CSS” box.
#header-menu .menu { text-align: center; }
#header-menu ul.menu li { display: inline-block; float: none; }
#header-menu ul.menu a { text-align: left; }
2.- Add a background image in the menu space.
You can change the background color from “Appearance => Theme Options => Color Options”. We really don’t recommend adding background image. It will make your site heavy. You can add the image url and color code in below css and then add it in “Appearance => Theme Options => Custom CSS” box
#header-menu #access { background: url("yourimageurl") #222; }
3.- Add the search at the right of the principal menu
— Sorry, there is no option to add search at the right of primary menu. You can add search above it at “Header Right Sidebar” from “Appearance => Widget” or in your other sidebars. This will need to change the theme functions for which you need to hire customizer and then ask him/her to build child theme and add search in primary menu.
4.- Change the icon of search.
— Upload the new search icon from “Media => Add New” and then copy your new search icon image url and in the following css add in the url and then add it in “Appearance => Theme Options => Custom CSS” box
.widget_catchevolution_social_search_widget #social-search #s { background-image: url("imageurl"); }