Right, now that I have a moment to properly respond, I might as well try and make most of it:
1. Equipment and InventoryThe equipment part seems find to me. It makes sense to also have equipment take up inventory space, but I wonder if that isn't just taking it too far. Especially when:
To balance this out, the inventory will be made bigger.
Why bother at all, then? To translate a beautiful Dutch saying, it'll be 'fucking around in the margins'. This might depend on the inventory management part, though, since I share emulord's Tetris Stance. Thinking back to Diablo II: "Hell yes I can carry that dagger, it fits right below the gothic plate. Now turn, damn you!". It'll be micromanagement all over again, just in a different guise.
Alternatives? First thing that springs to mind is Baldur's Gate and other D&D based games, where you have a limited number of slots and a maximum weight you are able to carry. Not the prettiest solution, but possibly reworkable. I'm sure there are those among us with better alternatives.
Say it, baby; say it, babyyyyyyyyyyy!2. AmmoI need a solution that did include the strategy of ammo management, but took away the need of fiddling with a lot of items.
I completely fail to see how your proposed solution changes anything. In the end you'll still be deciding whether you'll be sacrificing the space for Ammo Type A, Ammo Type B, a medkit or an armor. You'll just have it in boxes instead of in stacks.
Give the player 2 ammo slots, to be assigned to a given type of ammo at game start (or rather, pre-assigned). Give the player a Doomish max ammo count for each type. Screw inventory. Allow the player to gain ammo slots (increasing the number of ammo types the player can use) to be assigned at the moment they are encountered. They can be used for ammo for new types of weapon, or for alternative ammo types for available weapons. Restrict the ammo the player can choose to assign to elements he's encountered in the game. Use the DoomRL Medal/Badge system for this, so that the choices are expanded after each game. After go-live, you can even update with new types of ammo.
To increase ammo slot capacity, use something similar to Doom's Backpack.
3. Ammo typesSee 2.
4. Items on floorTough one. As I said before, chances of accidentally dropping stuff should be slim to none, but I agree that it would really work well on the game's pace. As an aside, if you eliminate the need for the player to go back to previous levels to flip a switch/access a terminal/destroy a power generator/etc as well, this choice would make backtracking completely redundant. Backtracking's not very 90's FPS anyway (:
This:
2) I don't think this mechanic would alleviate backtracking much anyway, as players will still backtrack to get at the corpses, lockers, boxes, etc...
constitutes a valid point, too. My Completionist OCD levels would run high enough as to carry as little stuff as possible up until the end of the level, then go back and fill up my inventory as tediously efficient as possible. Pace? What pace?
And I'm assuming your theory means stashing stuff in said lockers is off-limits, since it would eliminate the thought behind your idea in a spectacularly annoying fashion. And being able to take something from a locker without being able to put anything back in almost always smells of poor design.
There. That about sums it up so far. I do so hope I said something stupid that makes other people come up with brilliant stuff again (: