There are already 2 sort functions for your inventory "Automatic", i believe this is the random one you referred to, there is a very strict pattern for it, consumables then gear which sorts out much like the AH does RA weapons, ammo, reg weapons, head gear etc etc. and then "Manual" which lets you put anything anywhere in any order, It's time consuming to put everything into a spot manually every time you change gear,but i don't think putting anything alphabetically would really help all that much. I rather dislike the idea of having my Ziska's crossbow at the bottom of the list because it starts with Z rather then at the top because it's a RA weapon. I think you have not really paid much attention to where the "Automatic" sort actually PUTS your gear, and in what order. For spells and such i HATE the way the Automatic sort puts them, there again though an aphabetic sort would not be terribly useful, there are too many bar- spells that would be incredibly close together and at the very top of the list for any job that has them. I "Manually" sorted my spells by element and most used for example, Cure 1-6 at the top, then curaga 1-4 regen 1-4 refresh raise 1-3 pro 1-5 protectra 1-5 shell 1-5 shellra 1-5 etc. You can do this same thing with your gear by the way. These lists do not resort unless you tell them to. My blu spell list is even more complex, but that would be a long post so. In short i think the current method for sorting your inventory is fine, if you want to sort all your stuff your way, alphebetically or what ever use the "Manual" sort function the game already has.
In regards to the KI functions, i have played when there was NO distinction between any of the KI's. There was a master list that said "Key Items" THIS WAS HORRIBLE. It had a list, not in alphabetical order but by the a similar method where maps where at the bottom and i have no idea how the rest of the list was sorted, it all seemed very very random. I think SE made HUGE strides by making the differentiated lists we have today. However, we DO need more categories introduced, such as Abyssites, Atma's, Current Quest KI's, Battlefield KI's, Forced spawn KI's/Trophy KI's or something of that nature there are too many items under "Temporary Key Items" it takes eons to sort through.
As for storage not being accessed from a rent-a-room.... i would hate to see this for the simple fact that it would cut out every reason for ever having to return to one's home nation, unless you wanted to Outpost or something like that, i think the reason they did this is the realworld mechanic, you do not have all the 'furnishings' you do at your home mog house in your rent a room, so there fore you only get access to what is stored in your 'luggage' none storage inventory. Your rent a room is like being on vacation and you can't take everrrrything with you so storage is what you have to leave behind like your 50" plasma tv in real life or whatever you have lol. That's my take on things anyway.