Today, I finished the final details to create a json file exactly structured as the first version project. Also, the previous version was merged with the data produced by the PHP script (as well, other path access routes were solved in order to make the site work), so, finally, the result was an identical local site as the one host on the server.
Previous code was calling wordpress data first 100 posts, but when future entries exceed 100 posts, previous code would not retrieved all the data, by applying a mounted function on vue and making another call to the data whenever the current called equals 100 posts.
This was updated on every taxonomy and post.
Errors were found on the site, when first using the search bar to filter the display, and then using the alphabetic bar to scroll the page. The website reloaded the model (making the filters empty), by forgetting about an specific current key on the router view this issue was solved.