Topic.

Can you even add that enchantment to anything but a shield?

You should be able to add the Fortify Block to select items, just as any other enchantment. Which ones? I am unsure of.

Those Fortify Block enchantments will effect the skill level. Thus it will be for weapons as well as a shield.

So, short answer: Yes.

I think the enchantment only applies to shield blocking. Since the description reads, "Increases blocking with a shield by __%" or something like that.

Fortify Block is Fortify Block. It affects both shield and weapons. The wording in the description is misleading.

The items that can be enchanted are Neck, Ring, Shield and Gloves.

what does the fortify light/heavy armor do

Increases the associated skill level.