It may be a little confusing, but that "OR" is correct. Let me restate that rule and maybe that will help.
Scale, studded or brigandine can only be counted as armor if:
2/3rds of the target area covered by the piece of armor is made of armor-grade metal or leather
OR
the studs, rings or plates made of armor grade leather or metal are no more than 1/2 inch apart across the area covered by the piece of armor
Composite armor can be backed by cloth, light suede or any other non-armor grade material, so no, the backing doesn't need to be armor grade itself - that is what the studs, rings or plates are for.
Your question in the middle about different pieces of armor doesn't apply to any of this, as each piece is judged separately under both rule 3.3 and the Addendum A rules for inspecting that armor that you quoted from.
In addition to all of that, to be Armor, the item must meet all of the requirements below.
3.3. Armor
3.3.1. Armor confers one additional hit to the Target Area covered by the Armor. Multiple pieces of Armor on the same Target Area only confer a single hit. A single piece of Armor covering multiple areas confer a hit on each Target Area covered.
3.3.2. Armor only protects areas covered.
3.3.3. Armor must be of a size to cover a significant portion (approximately one-third) of a Target Area. Armor extending continuously from another Target Area is not required to significantly cover neighboring Target Areas to count as Armor.
3.3.4. Weapons that strike both Armored and unarmored Target Areas are considered to have hit the unarmored Target Area.
3.3.5. The presence of Armor must be easily discernable to count as Armor.
If you have more question, you can either edit your original post or PM me. I'll then edit this to clarify my points or to address your new ones.