Hi,
I was wondering if the search method search in content built with page builder/block?
If yes, can I use the “score” option on block fields name?
If yes, what if two different blocks have two different field with the same name?
Thanks for your clarifications 
By default, search takes into account in all fields, no matter what field type.
No, it works on a field basis, so the blocks field as a whole, not individual blocks or fields inside a block.
Note that there is also a $blocks->search() method, which might be helpful if you want to create a custom search.
Can the search method return a page if it find a word which is stored in a structure field itself included in a block?