1. Armor points. Exactly how they'll be used isn't yet concretely defined, but you can assume they'll function like armor points in other games.
2. Items that don't have affiliations listed aren't currently being produced, so you won't be able to acquire one yet. But there's no combat yet so hopefully you're in no hurry.
3. You can brawl anywhere, if you have access to a brawler. You just talk to them and select the options to fight rather than run. He can brawl 4 times a day; you can brawl 5 times a day.
4. See #2. It's also worth noting that crafting kits don't do anything yet, and weapons can only be constructed by weapon production factions at this time.
Some people do possess some rare items however they are (unsurprisingly) very rare, probably not for sale and if they are, more expensive then you can afford/would want to pay anyway. It's best to assume you can't get a hold of any.