So if you throw in a crappy, Tier II sword, you can expect that the monster won't do much damage?

nope this is a false assumption. No matter what Tier you throw in , it can be very easy, or very hard at times. Ive had tier I items hit me for 500+ its a gamble when welling, but generally with the right heal and a decent attack charm you can do most of them.

So how is it logical that the well monster uses the item you drop in? If they can be difficult or easy, given the same item, how does that work out?

there's some sort of balancing that allows the monster to be powerful no matter what.

If you throw in a tier 1 sword you'll notice that it hits for high/low hits with he occasional huge crit, showing that its using a sword. and you'll notice some of the mods of the time will work for the monster too.

The balancing if anything is tweaked that really low tier items will be even harder than the higher items.

Yea, that's what I'd say.

I threw in a copper longsword, got hit for 2k+ twice.

It all varies.

That is very scary. Especially if that happens on HC!