Is there a MediaWiki page that manages the order?
nope. moreover, u can't even touch standard menu items by script, because of terms of use.
Yes you're allowed to. :)
@Count of Howard - http://community.wikia.com/wiki/Help:Customization_policy
"Other customization may only be implemented via Theme Designer, with the following exceptions:
Ok, do you know the code? It would be greatly appreciated. :)
move history on top:
$('.wds-dropdown .wds-dropdown__content .wds-list #ca-history').closest('li').prependTo($('.wds-dropdown .wds-dropdown__content .wds-list'));
change #ca-history to element id u need to move. if u need move to bottom, then change prependTo to appendTo.