I have problems when I test locally in a browser.
The problem is that I have javascript on a subpage and this does not work when testing locally.
When I deploy and test then the javascript on the subpage works fine.
Javascript on the main page (index.html) works fine when testing locally.

Got a link? The script shouldn't work different on any sub page if it's put on the page exactly the same as it is on the index page. Might be you put it inside a different area or something and it's having to load other things prior to the script or visa versa. Give us a link so we can see the live pages you are talking about and tell us which script is in question and we'll see if we can give you a hand here.