Random feedback as a player, not as a dev:
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
2. god no, this would break all my equipment routines... I remember who needs to get what equipment based on their position in the craft, not based on their name or some random RPG stuff, I need to always start on position 1 (and can do everything blindly without even looking at their names)... otherwise I will spend more time figuring out where did I randomly start this time than what I spend on actual equipping
3.1 no thank you, I don't want items appearing/disappearing and changing positions each time I press a key, distracting as heck!
3.2 ok this one I answer as a dev: preserving vanilla look is important, not just "other than"... and user options will be added only for things with a fifty-fifty-ish user preference... I am not adding user options for one user, or even 10 users, or even 50... I need to be 100% convinced that an option appeals to a significant percentage of xcom players before I even start considering it... and in this case, I'm not convinced... btw. such option existed in the past and it was removed (on December 24th 2016) because it was unpopular
4.1 right click is already taken (prime); and shift+left click is also taken (quick unload)
4.2 ctrl+alt+X moves everything unequipped back to base