2.Suggested change: You click the icon showing the number of spell slots, it shows spells for only that level. This is because these icons only show you remaining slots for each level, there is a seperate icon for each collection of spell slots, each icon representing each level (do you follow yet?). You click the icon for spell slots remaining, it brings up a pop up menu with only spells that will use that spell slot. This will only show level 2 spells when you click on the "Level 2 Spell slots remaining" icon.
3. I click the (level 2 spell slots) it shows ONLY level 2 spells. I dont see any level 1 spells in this list or level 3 spells, simply level 2 spells.
4. The hotbar is no longer used to store every spell. The hotbar is used for whatever the player wants, items, cantrips, favorite spell from whatever level. Every spell is within 3 clicks of the spell slot icon, and the levels are seperated via the separate icons representing the remaining spell slots for that level. You want to cast a level 1 spell, you click the icon for level 1 spells that already exists in the game right now and just select the spell.
I wholly agree with this concept. I was even going to go so far as to suggest the top bar of the two standard hotbars be used as a "Class Skills Bar" but the method you outlined might be better yet.
Default spell level selection to Shift + # corresponding with spell level, or click of course. It opens the menu you described by either hotkey or click, allows quick oversight of how many of each spell is remaining, cleans up the hot bar, simplifies spell organization and would be a huge boon to the visual clutter of the hot bar in general. Even if the hotbar is still full, it can be full of interesting gadgets, or other items and save a whole lot of space giving spells their own little area.
What's best about this, is that people could just drag the spells straight from their book if they so choose to continue the current method.
I can imagine making this functionality work with pouches and backpacks too- so that when you have one on your hotbar, it opens a window the same way and displays the container's items to you. This makes potions, arrows, scrolls, ANYTHING sortable at your will. If you allow bags to be renamed so that the mouse-hover gives a tooltip of your custom tag, then you're really on to something. Currently, it does sort of work this way- but it doesn't feel good that's for sure.
A real adventurer would have a lot of containers anyways, right? A lot of bags, pouches, sacks full of various dusts. It's realistic to push the use of those containers for organization. Same idea for the spells.
TLDR;
Create nested menus for spells using the already implemented spell-slot level counters
-Bonus points if they're hotkeyed by default to something snappy, like [Shift + # of spell]
Create hotbar-friendly nested menus for containers (pouches, backpacks, etc)
-Bonus points if the containers can be non-intrusively renamed or recolored in some way