Last question, when I’ll create more TablePress tables will I have to re-generate/re-create the index table or will it be fed automatically when new tables are created ?
Indeed that topic should help you with indexing the tablepress tables.
Once you create the tables and add the table shortcodes to a post or custom post type and save the editor screen, the post content is indexed automatically, including the tables – you don’t need to recreate the index.