If you create a 20-foot cube, and someone gets stuck in the first 5ft.. when they succeed on Strength to no longer be restrained, does that mean they can move through the cube freely for the remainder of their turn?

RAW, yes, but probably up to the DM to rule that.

Actually, by RAW, no. The very first effect the spell describes is that the webs are difficult terrain. The spell then goes on to describe the restrained condition and how a creature can break out of it, but the strength saving throw doesn't change the fact that the area of the spell is difficult terrain.

For some reason the program won't let me attuned the wand. I am a wizard.

Quote from Schuyd >>

For some reason the program won't let me attuned the wand. I am a wizard.

 have you marked it "Active" on your inventory list?

Does a Web spell from the wand require Concentration?

I’m trying to pick random magic items to describe as daelkyr creations so I’m better at that if I ever get to run an Eberron campaign.

“The Crawling Queen has influence over spiders, a powerful enough influence to create this wand (though some insist that the wand’s true creator, or at least a collaborator, was Dyrrn, the Corrupter). It seems like an ordinary length of wood until it’s used, at which point several spiders spill from the wand, and you partially mutate into an enormous spider. You regurgitate massive amounts of webbing in this state, after which you revert, with the spiders disappearing”

Do the webs cast through wand of web require concentration?

Since you are casting the web spell and it doesnt say it doesnt require concentration, i would say so

Can the Wand of Web also act as an arcane focus for spellcasting, particularly a sorcerer?

If a magic item lets you cast a spell that requires concentration, then yes. It's just granting you access to a spell you may, or may not, already have access to, and possibly providing the fuel (charges instead of your spell slots.) The concentration requirement is not explicitly stated in item's description, but it is clearly stated elsewhere in the PHB that this is how magic items work.

However, if a magic item produces an effect but doesn't say it's casting a specific spell, then any concentration considerations must be explicitly stated in the item's description. And if it doesn't say it requires concentration, then it doesn't! See Wand of Paralysis for an example. But if an item says "as if concentrating on a spell", then all the concentration rules are in effect even if it's not a spell.

Could you technically swing with this item

Why does this require attunement but other uncommon wands like a wand of magic missiles doesn't?