I have found where the first and second problems come from… but it makes no sense !
I applied display:flex; to the ul.navbar-nav (à paraitre -> tout savoir), because I need the menu to take all the width of the row.
I dont know why, but this specific lines results in the .sm-collapsible applied on load to the ul.navbar-nav element.
And if this class is not applied on desktop, then my two first problems are resolved.
But how is the display style messing with the JS ? It doesn’t make sense !