I already have 100 in heavy armor and say I use some enchanted boots of the knight for +15

You get 115 heavy armor skill as long as you wear the boots

ok to rephrase that, does your armor rating get higher on items because of this?

easy to find out isn't it? just try it out?

It works with the Gift of Charity, too. Tiberius often finds himself having 106 Speech. Kind of awesome, really.

Yes.

It's honestly not worth using the fortify heavy/light armor enchantments though, they just don't provide enough of a bonus compared to other enchantments.

It depends on the skill. Fortify Armor skills just give a slight bonus to AR. Foritfy Smithing adds directly to the improvement from Tempering, which is why it's so popular. (I just hate crafting.) Fortify any magic school lowers the casting cost, no matter how high the actual skill, and Fortify Weapon Skills go directly to damage. So, what Bobjim123 said, it's one of the worst fortify skill enchantments in the game, along with Fortify Block.

Well fortify block is okay, but I'm happy with the base block level and my skill. All weapons block at ~60%, an iron shield blocks at ~53% and a daedric shield blocks at ~63% at block level 100. I don't need any more damage reduction than that, on master.

I imagine some power gamers do though. A fortify block enchantment of 35% ish will give you the maximum 85% damage reduction when blocking with a daedric shield.