Yes on edition but on save the display under the ajax zone stays the same until the reloading of the page

That's completely normal. Fields outside of an ajax edit do not update. There is not and never has been any such functionality. There are no plans for such functionality. One workaround to this is to use the new full tab ajax editing to ajax edit the entire tab instead of field by field. This will refresh the entire tabs display.

BTW can you tell me why an empty query field does not display its icons or info text ?

Regular query fields rendering works basically the same as a custom html field. It has no storage and is purely for display only. It has no edit behavior so it has no edit icons and there's no input to bind the description to. They do support Layout parameters though so you can use that to add extra descriptive text if you wanted.

Layout doesn't care if a field is empty or not. It just adds to the output. You can even prevent a field from being empty entirely using layout parameters.