I've heard people who run games where they don't count armor that you wear in your carry weight and people who do. I'm wondering what the RAW would state - does it count?
From the SRD:
Yes, they count.
I think this question and many of your other questions can be answered by the general rule of RPG systems.
If the game doesn't say there's an exception, there's not an exception. The way the game works is to lay out general rules, and then state explicit exceptions. If the exception isn't stated, then the general rule applies.