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FINALY (or close to)

Thanks Sally-CJ https://wordpress.stackexchange.com/users/137402/sally-cj As soon as can vote, i do it one for you.

I could get rid of My problem Because of 2 main things :

• Using $_POST instead of $_GET for my filters form
• Using pre_get_posts to modify WP_Query looks better than making a custom query

JSFIDDLE

• The custom post type & taxonomy(s) function(s) : https://jsfiddle.net/gelcin/8hx5vqe4/1/
• The Filters block inserted througth get_template_file : https://jsfiddle.net/gelcin/myodq3up/
• The header of the page content (outings-header.php, resume of informations selected in filter form) inserted througth get_template_file : https://jsfiddle.net/gelcin/wmgr5s20/1/

In order to help -or not-, i've found this thread where he could make it works by calling paginate_links in "success" of its ajax function. (he try the same but in ajax).

https://grafikart.fr/forum/23564