So item lists in your inventory appear to be alphabetical. Can they be manually organized? As it stands similar items of different materials can be hard to keep track of. I'd rather see "Armor: Iron" and "Armor: Steel" so I can know what I'm carrying by item type.

Not currently with the existing poopy UI. Your best bet is to take up and invest in Enchanting so you can change the names of things...My Armor is AA Archer Gloves, my weapon is AW Soul Trap Bow. Anything I am not wearing is well, junk anyways though!

The inventory that you hold on you doesnt bother me that much as I try to keep on top of it as much as possible, what annoys me is the inventory in chests. As you all know your personal inventory is sorted into Armor, Weapons, Keys, Books, Potions etc while chests are just sorted as All. So if I want something like an Ebony Ingot for example I have to hunt through a massive list of items for ages, its worse when its something that begins with a letter near the end of the alphabet. Why couldnt chests also be sorted into sections like your personal inventory? I try to keep a chest for Armour and a chest for Weapons and a chest for Ingredients etc but sometimes its easy to make a mistake and I wish their was a simpler system.

nope.
the inventory screens on player, companion, or container is very cumbersome and annoying.

There's a mod like that on the nexus, i think it's called headbomb's better sorting and another one called container categorization, Here's sum links

http://www.skyrimnexus.com/downloads/file.php?id=2730
http://www.skyrimnexus.com/downloads/file.php?id=1227

Hope they help.