front end publishing not working on front-end page

thanks to @TheDeadMedic, I found the solution.
I used reserved terms, and that’s why WordPress interpreted my inputs as query parameters.

so for example with my categorys, I had to change my classes in my form :

  'post_category' =>  array($_POST['cat']), // Usable for custom taxonomies too

by

  'post_category' =>  array($_POST['my_cat']), // Usable for custom taxonomies too

and in my form the class name “cat” by “my_cat”.

I had to change this every time I used a reserved term.

and now it works perfectly fine !