Blocking mechanics and armour cap

Basically, I'm looking to understand how shields and blocking works within the mechanics of combat. I'll try and keep the question as brief as possible, but I'm looking for working so I can plan my characters as best as possible.

For my current character I'm trying to run the game using only a set of steel armour that I'll improve over time. At the moment the armour value without the shield is 135. The shield has an armour value of 30, giving a normal total of 165.

So, if I take a hit, it's obvious that without the shield I apply the armour value of 135. If I equip the shield and take a hit (without blocking) do I take that at 135 or 165? If I block the hit is there a separate modifier for the block skill, or is it now that the 165 occurs? (Block is 28 with 1st Shield Wall perk).

In the future I'll (hopefully) get to a point where I reach the armour cap. As I occasionally use a bow I'll try and make the normal four pieces hit the max (567) so I still get the full 80% reduction. If I take a hit now with or without the shield I've reached the limit of the damage reduction, but does blocking now give an extra reduction?

With regards to weapons, as there is no limit I'll eventually end up with a dragonbone sword or similar. Is the damage reduced by blocking dependent on the armour value of the shield? Is this capped?

I know this seems like a lot of questions, but ultimately it leads me to ask, whilst I think I can max out the steel armour without a shield, will I want to create a shield of a different type (daedric?) to max out my protection, or else will the steel shield (legendary obviously) provide this?

Equipping a shield improves your armor rating, blocking is not required to take advantage of the improved armor protection provided by a shield. When you block, damage is first reduced according to the blocking formula below up to an 85% reduction, then your armor further reduces incoming damage.

Blocked Damage = (0.45 + (0.27 * ((shield base armor rating * (1 + Skill/100))/100))) * (1 + 0.1 for each Shield Wall perk)

Without a shield, the formula goes like this

Blocked Damage = (0.30 + (.02 * (1 + Skill/100)/100)) * (1 + 0.1 for each Shield Wall perk)

Note: these formulas are approximated from in-game testing, may not be 100% correct.