1 - How to remove the headband just under the menu ?
2 - the menu link “realisations” make a link to a category. When we clic on it, how to do to make disappear the sidebar ?
4 - can we fix the footer in the bottom
5 - How can we left center the menu (in the example Tarifs, a propos, realisations ?
Not an issue at all. Both Shapely and Illdy theme that you are using on your site are developed by Colorlib.
We generally answer questions in the support forums in same day but as we have holidays on Saturday and Sunday therefore we get a bit load on Monday to answer all questions so some questions gets delayed.