Hi,
The pro version has a slightly different query structure, given the plugins are completely separate in terms of performance as well as features.
There is actually difference in keywords order, it makes a difference. First keywords and second, third etc.. are weighted a bit differently, the first keyword is has a bit bigger impact. In this specific case “benefícios da abóbora” and “benefícios abóbora” also differs in a keyword “da”. If you want, you can make an exception for this keyword to be ignored completely, and then the search phrases become equal: https://i.imgur.com/BX3VS0P.png
As for the custom CSS, the lite version has a bit different strucute and node names. Replacing asl_ with asp_ and #ajaxsearchlite with #ajaxsearchpro will mosty help. While custom coding is beyond our support, I did a few replacments for you, this is the corrected version for PRO. You will have to test for the rule specificities if some of them does not apply.
The correct code for the Pro version for the nav menu (search ID=1):
// generate_navigation_search_menu_item_output
add_filter( 'generate_navigation_search_menu_item_output', function () {
echo do_shortcode( '[wd_asp id=1]' ) ;
} );