My question is about the enchantments similar to that of the silver swords. They don't require any recharges, the enchantment is just always there. Is there any enchantments like this that you can actually place on any weapons?

I think it's just a few set items. Wuuthrad is one...but you can't take the enchantments

does that apply to all the enchantments like this?

Skill enchantments are the only ones that dont need recharging

I know you can't use those two enchantments. Are there even any other items that behave this way?

there are a few other weapons ingame that have enchantments that don't need recharging

we have Horksbane from Dragonborn, which does extra damage to Horkers
the Poachers axe, which does extra damage to animals
and the Briarheat Geis (which can only be obtained through console commands), which does Extra damage against all Nords

however, none can be disenchanted

Poacher's Axe and Briarheart Geis actually can be disenchanted, but I don't think the enchantment actually works on anything but the original weapon.

I've tried enchanting swords with the Briarheart Geis enchantment taken from the console-conjured weapon, and either the extra damage is so pitiful it makes no difference/doesn't show or it just plain didn't work.

Don't know about horksbane but I have disenchanted the poachers axe and briarheart geis before, disenchanted the notched pickaxe as well.

well then, I stand corrected

Bit off topic, but you do know you can enchant silver weapons? It won't show up, the extra undead damage listing takes precedence, but it still works. There's also a bow similar to the poacher's axe but far superior, which can't be disenchanted:

Zephyr the bow is another with a special enchantment that doesn't require recharging.