Does that mean that creatures wearing clothing also cannot pass, since their clothing is considered nonliving matter?
Yes
In that case, isn't 2 a stronger setting than 3, despite costing less charges?
No, because owlbears and dragons don't wear clothes.
You will never have to worry about passwall targeting the barrier
Passwall's description states (emphasis mine):
A passage appears at a point of your choice that you can see on a wooden, plaster, or stone surface (such as a wall, a ceiling, or a floor) within range, and lasts for the Duration.
The surface of the Cube of Force creates "a barrier of Invisible force". If the caster cannot see the barrier, typically requiring a spell like See Invisibility, then they cannot target the barrier. But even if they can see it, the barrier isn't wood, plaster, or stone. Thus, it is an invalid target for Passwall as far as a direct cast.
With that in mind, the only thing we need to worry about is the cube's barrier overlapping with an opening, created by Passwall, on a different surface. In that case, Passwall's effect has nothing to do with opening a passage in anything other than the surface it was originally cast on. Thus, we don't have to worry about any effect applying to the cube, aside from the specific description in the cube's text.
The cube loses 1d6 charges because the item's description says it does, but no hole is created in the barrier because the cube didn't say that would happen, and the Passwall spell wasn't cast on the barrier.
Repeatedly colliding with a Wall of Fire will continue to drain charges
The cube's description only states:
The cube loses charges when the barrier is targeted by certain spells or comes into contact with certain spell or magic item effects
The text makes no mention of "The first time the barrier is targeted..." in contrast to many other effects that do use this language. For example Wall of Fire itself, which says:
A creature takes the same damage when it enters the wall for the first time on a turn or ends its turn there.
From this, we can determine that no matter how many times you run into the same Wall of Fire, the cube will continually lose charges, because there is no exception which states that the drain was only meant to be applied one time.
Best Answer
Cube of Force(option 4) does not stop Banishment.
snippets of Cube of Force
Nothing in the item's description implies that spells can't be cast from within the cube (compared to AntiMagic Field). Banishment doesn't "send out" an effect, so there's no reason that the two should interact.
The archmagi would walk in and cast Banishment. Pending a failed save, the player who initiated the Cube of Force would blink out of existence, along with their cube effect. Then 1 minute later, they would reappear, without the cubes effect, as more than 1 minute has passed since the Cube of Force was activated.
PS - Though this doesn't apply to this exact interaction, I'm not sure if you could teleport from inside of the cube to outside or vice versa (think Dimension Door). My inclination is to say, that you could, as you're bypassing the barrier. Much as if it were a physical wall. Wizards can't walk through walls, but they can teleport to the other side.