1.1 I almost never click "scroll right" even in biggest mods, saying it's the most clicked button is... subjective. I either have only the needed stuff (one screen is more than enough), or I use search/filter, or I do the equipment via pre-saved shortcuts
The other buttons in inventory screen are "Next Unit", "Previous Unit", "OK", "Unload", "Create a template" and "Apply template", and there's little reason to actually click them since they have shortcuts. So it isn't much of a stretch to assume that "Scroll right" is the most clicked one.
With two or three screens of equipment wheel scrolling would be way faster and more convenient than searching IMHO.
3.1 no thank you, I don't want items appearing/disappearing and changing positions each time I press a key, distracting as heck!
What if there were a small delay? If items would appear/disappear 200-600 ms after you finished typing (instead of refreshing on every keypress) it wouldn't be distracting.
4.1 right click is already taken (prime); and shift+left click is also taken (quick unload)
Sorry, I forgot about that. What about some other shortcut, like Alt + Left Click or Shift + Right Click?
4.2 ctrl+alt+X moves everything unequipped back to base
Wow. This is really helpful, thanks. Still, being able to remove search results could be useful.