In Epic 1.5 items (1) and (2) are about some nice improvements to the search suggestions. Is there any plan to include those changes to the "big" search box on the Special:Search page?
I discussed this with @JDrewniak (WMF), and suggested/requested it. However, there is now some very early discussion (just brainstorming at this point) about adding search suggestions to the big search box (i.e., you type "wikimedia" and it suggests the next word might be "commons" or "foundation"). It seems really complicated if not impossible to have a clean UI that supports both at once (though if someone could conquer that design challenge that would be awesome!). It might also be better not to add images and descriptions to the big search box only to take them away later, so we (Core and Search Platform) should probably coordinate on that before either moves forward with changes to the big search box.
OTOH, if it's not on your radar at the moment, then it's no harm, no foul.